/*******************************************************************************
 *                                                                              *
 * Author    :  Angus Johnson                                                   *
 * Version   :  6.4.2                                                           *
 * Date      :  27 February 2017                                                *
 * Website   :  http://www.angusj.com                                           *
 * Copyright :  Angus Johnson 2010-2017                                         *
 *                                                                              *
 * License:                                                                     *
 * Use, modification & distribution is subject to Boost Software License Ver 1. *
 * http://www.boost.org/LICENSE_1_0.txt                                         *
 *                                                                              *
 * Attributions:                                                                *
 * The code in this library is an extension of Bala Vatti's clipping algorithm: *
 * "A generic solution to polygon clipping"                                     *
 * Communications of the ACM, Vol 35, Issue 7 (July 1992) pp 56-63.             *
 * http://portal.acm.org/citation.cfm?id=129906                                 *
 *                                                                              *
 * Computer graphics and geometric modeling: implementation and algorithms      *
 * By Max K. Agoston                                                            *
 * Springer; 1 edition (January 4, 2005)                                        *
 * http://books.google.com/books?q=vatti+clipping+agoston                       *
 *                                                                              *
 * See also:                                                                    *
 * "Polygon Offsetting by Computing Winding Numbers"                            *
 * Paper no. DETC2005-85513 pp. 565-575                                         *
 * ASME 2005 International Design Engineering Technical Conferences             *
 * and Computers and Information in Engineering Conference (IDETC/CIE2005)      *
 * September 24-28, 2005 , Long Beach, California, USA                          *
 * http://www.me.berkeley.edu/~mcmains/pubs/DAC05OffsetPolygon.pdf              *
 *                                                                              *
 *******************************************************************************/

/*******************************************************************************
 *                                                                              *
 * This is a translation of the Delphi Clipper library and the naming style     *
 * used has retained a Delphi flavour.                                          *
 *                                                                              *
 *******************************************************************************/

#include "clipper.hpp"
#include <cmath>
#include <vector>
#include <algorithm>
#include <stdexcept>
#include <cstring>
#include <cstdlib>
#include <ostream>
#include <functional>

/* BRL-CAD warnings cause a problem in this file - turn off a couple so we
 * can build without having to make significant changes. */
#if defined(__GNUC__) && !defined(__clang__)
#  pragma GCC diagnostic push /* start new diagnostic pragma */
#  pragma GCC diagnostic ignored "-Wfloat-equal"
#  if (__GNUC__ >= 8)
#    pragma GCC diagnostic ignored "-Wclass-memaccess"
#  endif
#elif defined(__clang__)
#  pragma clang diagnostic push /* start new diagnostic pragma */
#  pragma clang diagnostic ignored "-Wfloat-equal"
#endif

namespace ClipperLib {

    static double const pi = 3.141592653589793238;
    static double const two_pi = pi *2;
    static double const def_arc_tolerance = 0.25;

    enum Direction { dRightToLeft, dLeftToRight };

    static int const Unassigned = -1;  //edge not currently 'owning' a solution
    static int const Skip = -2;        //edge that would otherwise close a path

#define HORIZONTAL (-1.0E+40)
#define TOLERANCE (1.0e-20)
#define NEAR_ZERO(val) (((val) > -TOLERANCE) && ((val) < TOLERANCE))

    struct TEdge {
	IntPoint Bot;
	IntPoint Curr; //current (updated for every new scanbeam)
	IntPoint Top;
	double Dx;
	PolyType PolyTyp;
	EdgeSide Side; //side only refers to current side of solution poly
	int WindDelta; //1 or -1 depending on winding direction
	int WindCnt;
	int WindCnt2; //winding count of the opposite polytype
	int OutIdx;
	TEdge *Next;
	TEdge *Prev;
	TEdge *NextInLML;
	TEdge *NextInAEL;
	TEdge *PrevInAEL;
	TEdge *NextInSEL;
	TEdge *PrevInSEL;
    };

    struct IntersectNode {
	TEdge          *Edge1;
	TEdge          *Edge2;
	IntPoint        Pt;
    };

    struct LocalMinimum {
	cInt          Y;
	TEdge        *LeftBound;
	TEdge        *RightBound;
    };

    struct OutPt;

    //OutRec: contains a path in the clipping solution. Edges in the AEL will
    //carry a pointer to an OutRec when they are part of the clipping solution.
    struct OutRec {
	int       Idx;
	bool      IsHole;
	bool      IsOpen;
	OutRec   *FirstLeft;  //see comments in clipper.pas
	PolyNode *PolyNd;
	OutPt    *Pts;
	OutPt    *BottomPt;
    };

    struct OutPt {
	int       Idx;
	IntPoint  Pt;
	OutPt    *Next;
	OutPt    *Prev;
    };

    struct Join {
	OutPt    *OutPt1;
	OutPt    *OutPt2;
	IntPoint  OffPt;
    };

    struct LocMinSorter
    {
	inline bool operator()(const LocalMinimum& locMin1, const LocalMinimum& locMin2)
	{
	    return locMin2.Y < locMin1.Y;
	}
    };

    //------------------------------------------------------------------------------
    //------------------------------------------------------------------------------

    inline cInt Round(double val)
    {
	if ((val < 0)) return static_cast<cInt>(val - 0.5);
	else return static_cast<cInt>(val + 0.5);
    }
    //------------------------------------------------------------------------------

    inline cInt Abs(cInt val)
    {
	return val < 0 ? -val : val;
    }

    //------------------------------------------------------------------------------
    // PolyTree methods ...
    //------------------------------------------------------------------------------

    void PolyTree::Clear()
    {
	for (PolyNodes::size_type i = 0; i < AllNodes.size(); ++i)
	    delete AllNodes[i];
	AllNodes.resize(0);
	Childs.resize(0);
    }
    //------------------------------------------------------------------------------

    PolyNode* PolyTree::GetFirst() const
    {
	if (!Childs.empty())
	    return Childs[0];
	else
	    return 0;
    }
    //------------------------------------------------------------------------------

    int PolyTree::Total() const
    {
	int result = (int)AllNodes.size();
	//with negative offsets, ignore the hidden outer polygon ...
	if (result > 0 && Childs[0] != AllNodes[0]) result--;
	return result;
    }

    //------------------------------------------------------------------------------
    // PolyNode methods ...
    //------------------------------------------------------------------------------

    PolyNode::PolyNode(): Parent(0), Index(0), m_IsOpen(false)
    {
    }
    //------------------------------------------------------------------------------

    int PolyNode::ChildCount() const
    {
	return (int)Childs.size();
    }
    //------------------------------------------------------------------------------

    void PolyNode::AddChild(PolyNode& child)
    {
	unsigned cnt = (unsigned)Childs.size();
	Childs.push_back(&child);
	child.Parent = this;
	child.Index = cnt;
    }
    //------------------------------------------------------------------------------

    PolyNode* PolyNode::GetNext() const
    {
	if (!Childs.empty())
	    return Childs[0];
	else
	    return GetNextSiblingUp();
    }
    //------------------------------------------------------------------------------

    PolyNode* PolyNode::GetNextSiblingUp() const
    {
	if (!Parent) //protects against PolyTree.GetNextSiblingUp()
	    return 0;
	else if (Index == Parent->Childs.size() - 1)
	    return Parent->GetNextSiblingUp();
	else
	    return Parent->Childs[Index + 1];
    }
    //------------------------------------------------------------------------------

    bool PolyNode::IsHole() const
    {
	bool result = true;
	PolyNode* node = Parent;
	while (node)
	{
	    result = !result;
	    node = node->Parent;
	}
	return result;
    }
    //------------------------------------------------------------------------------

    bool PolyNode::IsOpen() const
    {
	return m_IsOpen;
    }
    //------------------------------------------------------------------------------

#ifndef use_int32

    //------------------------------------------------------------------------------
    // Int128 class (enables safe math on signed 64bit integers)
    // eg Int128 val1((long64)9223372036854775807); //ie 2^63 -1
    //    Int128 val2((long64)9223372036854775807);
    //    Int128 val3 = val1 * val2;
    //    val3.AsString => "85070591730234615847396907784232501249" (8.5e+37)
    //------------------------------------------------------------------------------

    class Int128
    {
	public:
	    ulong64 lo;
	    long64 hi;

	    Int128(long64 _lo = 0)
	    {
		lo = (ulong64)_lo;
		if (_lo < 0)  hi = -1; else hi = 0;
	    }


	    Int128(const Int128 &val): lo(val.lo), hi(val.hi){}

	    Int128(const long64& _hi, const ulong64& _lo): lo(_lo), hi(_hi){}

	    Int128& operator = (const long64 &val)
	    {
		lo = (ulong64)val;
		if (val < 0) hi = -1; else hi = 0;
		return *this;
	    }

	    Int128& operator = (const Int128 &val)
	    {
		lo = val.lo;
		hi = val.hi;
		return *this;
	    }

	    bool operator == (const Int128 &val) const
	    {return (hi == val.hi && lo == val.lo);}

	    bool operator != (const Int128 &val) const
	    { return !(*this == val);}

	    bool operator > (const Int128 &val) const
	    {
		if (hi != val.hi)
		    return hi > val.hi;
		else
		    return lo > val.lo;
	    }

	    bool operator < (const Int128 &val) const
	    {
		if (hi != val.hi)
		    return hi < val.hi;
		else
		    return lo < val.lo;
	    }

	    bool operator >= (const Int128 &val) const
	    { return !(*this < val);}

	    bool operator <= (const Int128 &val) const
	    { return !(*this > val);}

	    Int128& operator += (const Int128 &rhs)
	    {
		hi += rhs.hi;
		lo += rhs.lo;
		if (lo < rhs.lo) hi++;
		return *this;
	    }

	    Int128 operator + (const Int128 &rhs) const
	    {
		Int128 result(*this);
		result+= rhs;
		return result;
	    }

	    Int128& operator -= (const Int128 &rhs)
	    {
		*this += -rhs;
		return *this;
	    }

	    Int128 operator - (const Int128 &rhs) const
	    {
		Int128 result(*this);
		result -= rhs;
		return result;
	    }

	    Int128 operator-() const //unary negation
	    {
		if (lo == 0)
		    return Int128(-hi, 0);
		else
		    return Int128(~hi, ~lo + 1);
	    }

	    operator double() const
	    {
		const double shift64 = 18446744073709551616.0; //2^64
		if (hi < 0)
		{
		    if (lo == 0) return (double)hi * shift64;
		    else return -(double)(~lo + ~hi * shift64);
		}
		else
		    return (double)(lo + hi * shift64);
	    }

    };
    //------------------------------------------------------------------------------

    Int128 Int128Mul (long64 lhs, long64 rhs)
    {
	bool negate = (lhs < 0) != (rhs < 0);

	if (lhs < 0) lhs = -lhs;
	ulong64 int1Hi = ulong64(lhs) >> 32;
	ulong64 int1Lo = ulong64(lhs & 0xFFFFFFFF);

	if (rhs < 0) rhs = -rhs;
	ulong64 int2Hi = ulong64(rhs) >> 32;
	ulong64 int2Lo = ulong64(rhs & 0xFFFFFFFF);

	//nb: see comments in clipper.pas
	ulong64 a = int1Hi * int2Hi;
	ulong64 b = int1Lo * int2Lo;
	ulong64 c = int1Hi * int2Lo + int1Lo * int2Hi;

	Int128 tmp;
	tmp.hi = long64(a + (c >> 32));
	tmp.lo = long64(c << 32);
	tmp.lo += long64(b);
	if (tmp.lo < b) tmp.hi++;
	if (negate) tmp = -tmp;
	return tmp;
    }
#endif

    //------------------------------------------------------------------------------
    // Miscellaneous global functions
    //------------------------------------------------------------------------------

    bool Orientation(const Path &poly)
    {
	return Area(poly) >= 0;
    }
    //------------------------------------------------------------------------------

    double Area(const Path &poly)
    {
	int size = (int)poly.size();
	if (size < 3) return 0;

	double a = 0;
	for (int i = 0, j = size -1; i < size; ++i)
	{
	    a += ((double)poly[j].X + poly[i].X) * ((double)poly[j].Y - poly[i].Y);
	    j = i;
	}
	return -a * 0.5;
    }
    //------------------------------------------------------------------------------

    double Area(const OutPt *op)
    {
	const OutPt *startOp = op;
	if (!op) return 0;
	double a = 0;
	do {
	    a +=  (double)(op->Prev->Pt.X + op->Pt.X) * (double)(op->Prev->Pt.Y - op->Pt.Y);
	    op = op->Next;
	} while (op != startOp);
	return a * 0.5;
    }
    //------------------------------------------------------------------------------

    double Area(const OutRec &outRec)
    {
	return Area(outRec.Pts);
    }
    //------------------------------------------------------------------------------

    bool PointIsVertex(const IntPoint &Pt, OutPt *pp)
    {
	OutPt *pp2 = pp;
	do
	{
	    if (pp2->Pt == Pt) return true;
	    pp2 = pp2->Next;
	}
	while (pp2 != pp);
	return false;
    }
    //------------------------------------------------------------------------------

    //See "The Point in Polygon Problem for Arbitrary Polygons" by Hormann & Agathos
    //http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.88.5498&rep=rep1&type=pdf
    int PointInPolygon(const IntPoint &pt, const Path &path)
    {
	//returns 0 if false, +1 if true, -1 if pt ON polygon boundary
	int result = 0;
	size_t cnt = path.size();
	if (cnt < 3) return 0;
	IntPoint ip = path[0];
	for(size_t i = 1; i <= cnt; ++i)
	{
	    IntPoint ipNext = (i == cnt ? path[0] : path[i]);
	    if (ipNext.Y == pt.Y)
	    {
		if ((ipNext.X == pt.X) || (ip.Y == pt.Y &&
			    ((ipNext.X > pt.X) == (ip.X < pt.X)))) return -1;
	    }
	    if ((ip.Y < pt.Y) != (ipNext.Y < pt.Y))
	    {
		if (ip.X >= pt.X)
		{
		    if (ipNext.X > pt.X) result = 1 - result;
		    else
		    {
			double d = (double)(ip.X - pt.X) * (ipNext.Y - pt.Y) -
			    (double)(ipNext.X - pt.X) * (ip.Y - pt.Y);
			if (!d) return -1;
			if ((d > 0) == (ipNext.Y > ip.Y)) result = 1 - result;
		    }
		} else
		{
		    if (ipNext.X > pt.X)
		    {
			double d = (double)(ip.X - pt.X) * (ipNext.Y - pt.Y) -
			    (double)(ipNext.X - pt.X) * (ip.Y - pt.Y);
			if (!d) return -1;
			if ((d > 0) == (ipNext.Y > ip.Y)) result = 1 - result;
		    }
		}
	    }
	    ip = ipNext;
	}
	return result;
    }
    //------------------------------------------------------------------------------

    int PointInPolygon (const IntPoint &pt, OutPt *op)
    {
	//returns 0 if false, +1 if true, -1 if pt ON polygon boundary
	int result = 0;
	OutPt* startOp = op;
	for(;;)
	{
	    if (op->Next->Pt.Y == pt.Y)
	    {
		if ((op->Next->Pt.X == pt.X) || (op->Pt.Y == pt.Y &&
			    ((op->Next->Pt.X > pt.X) == (op->Pt.X < pt.X)))) return -1;
	    }
	    if ((op->Pt.Y < pt.Y) != (op->Next->Pt.Y < pt.Y))
	    {
		if (op->Pt.X >= pt.X)
		{
		    if (op->Next->Pt.X > pt.X) result = 1 - result;
		    else
		    {
			double d = (double)(op->Pt.X - pt.X) * (op->Next->Pt.Y - pt.Y) -
			    (double)(op->Next->Pt.X - pt.X) * (op->Pt.Y - pt.Y);
			if (!d) return -1;
			if ((d > 0) == (op->Next->Pt.Y > op->Pt.Y)) result = 1 - result;
		    }
		} else
		{
		    if (op->Next->Pt.X > pt.X)
		    {
			double d = (double)(op->Pt.X - pt.X) * (op->Next->Pt.Y - pt.Y) -
			    (double)(op->Next->Pt.X - pt.X) * (op->Pt.Y - pt.Y);
			if (!d) return -1;
			if ((d > 0) == (op->Next->Pt.Y > op->Pt.Y)) result = 1 - result;
		    }
		}
	    }
	    op = op->Next;
	    if (startOp == op) break;
	}
	return result;
    }
    //------------------------------------------------------------------------------

    bool Poly2ContainsPoly1(OutPt *OutPt1, OutPt *OutPt2)
    {
	OutPt* op = OutPt1;
	do
	{
	    //nb: PointInPolygon returns 0 if false, +1 if true, -1 if pt on polygon
	    int res = PointInPolygon(op->Pt, OutPt2);
	    if (res >= 0) return res > 0;
	    op = op->Next;
	}
	while (op != OutPt1);
	return true;
    }
    //----------------------------------------------------------------------

    bool SlopesEqual(const TEdge &e1, const TEdge &e2, bool UseFullInt64Range)
    {
#ifndef use_int32
	if (UseFullInt64Range)
	    return Int128Mul(e1.Top.Y - e1.Bot.Y, e2.Top.X - e2.Bot.X) ==
		Int128Mul(e1.Top.X - e1.Bot.X, e2.Top.Y - e2.Bot.Y);
	else
#endif
	    return (e1.Top.Y - e1.Bot.Y) * (e2.Top.X - e2.Bot.X) ==
		(e1.Top.X - e1.Bot.X) * (e2.Top.Y - e2.Bot.Y);
    }
    //------------------------------------------------------------------------------

    bool SlopesEqual(const IntPoint pt1, const IntPoint pt2,
	    const IntPoint pt3, bool UseFullInt64Range)
    {
#ifndef use_int32
	if (UseFullInt64Range)
	    return Int128Mul(pt1.Y-pt2.Y, pt2.X-pt3.X) == Int128Mul(pt1.X-pt2.X, pt2.Y-pt3.Y);
	else
#endif
	    return (pt1.Y-pt2.Y)*(pt2.X-pt3.X) == (pt1.X-pt2.X)*(pt2.Y-pt3.Y);
    }
    //------------------------------------------------------------------------------

    bool SlopesEqual(const IntPoint pt1, const IntPoint pt2,
	    const IntPoint pt3, const IntPoint pt4, bool UseFullInt64Range)
    {
#ifndef use_int32
	if (UseFullInt64Range)
	    return Int128Mul(pt1.Y-pt2.Y, pt3.X-pt4.X) == Int128Mul(pt1.X-pt2.X, pt3.Y-pt4.Y);
	else
#endif
	    return (pt1.Y-pt2.Y)*(pt3.X-pt4.X) == (pt1.X-pt2.X)*(pt3.Y-pt4.Y);
    }
    //------------------------------------------------------------------------------

    inline bool IsHorizontal(TEdge &e)
    {
	return e.Dx == HORIZONTAL;
    }
    //------------------------------------------------------------------------------

    inline double GetDx(const IntPoint pt1, const IntPoint pt2)
    {
	return (pt1.Y == pt2.Y) ?
	    HORIZONTAL : (double)(pt2.X - pt1.X) / (pt2.Y - pt1.Y);
    }
    //---------------------------------------------------------------------------

    inline void SetDx(TEdge &e)
    {
	cInt dy  = (e.Top.Y - e.Bot.Y);
	if (dy == 0) e.Dx = HORIZONTAL;
	else e.Dx = (double)(e.Top.X - e.Bot.X) / dy;
    }
    //---------------------------------------------------------------------------

    inline void SwapSides(TEdge &Edge1, TEdge &Edge2)
    {
	EdgeSide Side =  Edge1.Side;
	Edge1.Side = Edge2.Side;
	Edge2.Side = Side;
    }
    //------------------------------------------------------------------------------

    inline void SwapPolyIndexes(TEdge &Edge1, TEdge &Edge2)
    {
	int OutIdx =  Edge1.OutIdx;
	Edge1.OutIdx = Edge2.OutIdx;
	Edge2.OutIdx = OutIdx;
    }
    //------------------------------------------------------------------------------

    inline cInt TopX(TEdge &edge, const cInt currentY)
    {
	return ( currentY == edge.Top.Y ) ?
	    edge.Top.X : edge.Bot.X + Round(edge.Dx *(currentY - edge.Bot.Y));
    }
    //------------------------------------------------------------------------------

    void IntersectPoint(TEdge &Edge1, TEdge &Edge2, IntPoint &ip)
    {
#ifdef use_xyz
	ip.Z = 0;
#endif

	double b1, b2;
	if (Edge1.Dx == Edge2.Dx)
	{
	    ip.Y = Edge1.Curr.Y;
	    ip.X = TopX(Edge1, ip.Y);
	    return;
	}
	else if (Edge1.Dx == 0)
	{
	    ip.X = Edge1.Bot.X;
	    if (IsHorizontal(Edge2))
		ip.Y = Edge2.Bot.Y;
	    else
	    {
		b2 = Edge2.Bot.Y - (Edge2.Bot.X / Edge2.Dx);
		ip.Y = Round(ip.X / Edge2.Dx + b2);
	    }
	}
	else if (Edge2.Dx == 0)
	{
	    ip.X = Edge2.Bot.X;
	    if (IsHorizontal(Edge1))
		ip.Y = Edge1.Bot.Y;
	    else
	    {
		b1 = Edge1.Bot.Y - (Edge1.Bot.X / Edge1.Dx);
		ip.Y = Round(ip.X / Edge1.Dx + b1);
	    }
	}
	else
	{
	    b1 = Edge1.Bot.X - Edge1.Bot.Y * Edge1.Dx;
	    b2 = Edge2.Bot.X - Edge2.Bot.Y * Edge2.Dx;
	    double q = (b2-b1) / (Edge1.Dx - Edge2.Dx);
	    ip.Y = Round(q);
	    if (std::fabs(Edge1.Dx) < std::fabs(Edge2.Dx))
		ip.X = Round(Edge1.Dx * q + b1);
	    else
		ip.X = Round(Edge2.Dx * q + b2);
	}

	if (ip.Y < Edge1.Top.Y || ip.Y < Edge2.Top.Y)
	{
	    if (Edge1.Top.Y > Edge2.Top.Y)
		ip.Y = Edge1.Top.Y;
	    else
		ip.Y = Edge2.Top.Y;
	    if (std::fabs(Edge1.Dx) < std::fabs(Edge2.Dx))
		ip.X = TopX(Edge1, ip.Y);
	    else
		ip.X = TopX(Edge2, ip.Y);
	}
	//finally, don't allow 'ip' to be BELOW curr.Y (ie bottom of scanbeam) ...
	if (ip.Y > Edge1.Curr.Y)
	{
	    ip.Y = Edge1.Curr.Y;
	    //use the more vertical edge to derive X ...
	    if (std::fabs(Edge1.Dx) > std::fabs(Edge2.Dx))
		ip.X = TopX(Edge2, ip.Y); else
		    ip.X = TopX(Edge1, ip.Y);
	}
    }
    //------------------------------------------------------------------------------

    void ReversePolyPtLinks(OutPt *pp)
    {
	if (!pp) return;
	OutPt *pp1, *pp2;
	pp1 = pp;
	do {
	    pp2 = pp1->Next;
	    pp1->Next = pp1->Prev;
	    pp1->Prev = pp2;
	    pp1 = pp2;
	} while( pp1 != pp );
    }
    //------------------------------------------------------------------------------

    void DisposeOutPts(OutPt*& pp)
    {
	if (pp == 0) return;
	pp->Prev->Next = 0;
	while( pp )
	{
	    OutPt *tmpPp = pp;
	    pp = pp->Next;
	    delete tmpPp;
	}
    }
    //------------------------------------------------------------------------------

    inline void InitEdge(TEdge* e, TEdge* eNext, TEdge* ePrev, const IntPoint& Pt)
    {
	std::memset(e, 0, sizeof(TEdge));
	e->Next = eNext;
	e->Prev = ePrev;
	e->Curr = Pt;
	e->OutIdx = Unassigned;
    }
    //------------------------------------------------------------------------------

    void InitEdge2(TEdge& e, PolyType Pt)
    {
	if (e.Curr.Y >= e.Next->Curr.Y)
	{
	    e.Bot = e.Curr;
	    e.Top = e.Next->Curr;
	} else
	{
	    e.Top = e.Curr;
	    e.Bot = e.Next->Curr;
	}
	SetDx(e);
	e.PolyTyp = Pt;
    }
    //------------------------------------------------------------------------------

    TEdge* RemoveEdge(TEdge* e)
    {
	//removes e from double_linked_list (but without removing from memory)
	e->Prev->Next = e->Next;
	e->Next->Prev = e->Prev;
	TEdge* result = e->Next;
	e->Prev = 0; //flag as removed (see ClipperBase.Clear)
	return result;
    }
    //------------------------------------------------------------------------------

    inline void ReverseHorizontal(TEdge &e)
    {
	//swap horizontal edges' Top and Bottom x's so they follow the natural
	//progression of the bounds - ie so their xbots will align with the
	//adjoining lower edge. [Helpful in the ProcessHorizontal() method.]
	std::swap(e.Top.X, e.Bot.X);
#ifdef use_xyz
	std::swap(e.Top.Z, e.Bot.Z);
#endif
    }
    //------------------------------------------------------------------------------

    void SwapPoints(IntPoint &pt1, IntPoint &pt2)
    {
	IntPoint tmp = pt1;
	pt1 = pt2;
	pt2 = tmp;
    }
    //------------------------------------------------------------------------------

    bool GetOverlapSegment(IntPoint pt1a, IntPoint pt1b, IntPoint pt2a,
	    IntPoint pt2b, IntPoint &pt1, IntPoint &pt2)
    {
	//precondition: segments are Collinear.
	if (Abs(pt1a.X - pt1b.X) > Abs(pt1a.Y - pt1b.Y))
	{
	    if (pt1a.X > pt1b.X) SwapPoints(pt1a, pt1b);
	    if (pt2a.X > pt2b.X) SwapPoints(pt2a, pt2b);
	    if (pt1a.X > pt2a.X) pt1 = pt1a; else pt1 = pt2a;
	    if (pt1b.X < pt2b.X) pt2 = pt1b; else pt2 = pt2b;
	    return pt1.X < pt2.X;
	} else
	{
	    if (pt1a.Y < pt1b.Y) SwapPoints(pt1a, pt1b);
	    if (pt2a.Y < pt2b.Y) SwapPoints(pt2a, pt2b);
	    if (pt1a.Y < pt2a.Y) pt1 = pt1a; else pt1 = pt2a;
	    if (pt1b.Y > pt2b.Y) pt2 = pt1b; else pt2 = pt2b;
	    return pt1.Y > pt2.Y;
	}
    }
    //------------------------------------------------------------------------------

    bool FirstIsBottomPt(const OutPt* btmPt1, const OutPt* btmPt2)
    {
	OutPt *p = btmPt1->Prev;
	while ((p->Pt == btmPt1->Pt) && (p != btmPt1)) p = p->Prev;
	double dx1p = std::fabs(GetDx(btmPt1->Pt, p->Pt));
	p = btmPt1->Next;
	while ((p->Pt == btmPt1->Pt) && (p != btmPt1)) p = p->Next;
	double dx1n = std::fabs(GetDx(btmPt1->Pt, p->Pt));

	p = btmPt2->Prev;
	while ((p->Pt == btmPt2->Pt) && (p != btmPt2)) p = p->Prev;
	double dx2p = std::fabs(GetDx(btmPt2->Pt, p->Pt));
	p = btmPt2->Next;
	while ((p->Pt == btmPt2->Pt) && (p != btmPt2)) p = p->Next;
	double dx2n = std::fabs(GetDx(btmPt2->Pt, p->Pt));

	if (std::max(dx1p, dx1n) == std::max(dx2p, dx2n) &&
		std::min(dx1p, dx1n) == std::min(dx2p, dx2n))
	    return Area(btmPt1) > 0; //if otherwise identical use orientation
	else
	    return (dx1p >= dx2p && dx1p >= dx2n) || (dx1n >= dx2p && dx1n >= dx2n);
    }
    //------------------------------------------------------------------------------

    OutPt* GetBottomPt(OutPt *pp)
    {
	OutPt* dups = 0;
	OutPt* p = pp->Next;
	while (p != pp)
	{
	    if (p->Pt.Y > pp->Pt.Y)
	    {
		pp = p;
		dups = 0;
	    }
	    else if (p->Pt.Y == pp->Pt.Y && p->Pt.X <= pp->Pt.X)
	    {
		if (p->Pt.X < pp->Pt.X)
		{
		    dups = 0;
		    pp = p;
		} else
		{
		    if (p->Next != pp && p->Prev != pp) dups = p;
		}
	    }
	    p = p->Next;
	}
	if (dups)
	{
	    //there appears to be at least 2 vertices at BottomPt so ...
	    while (dups != p)
	    {
		if (!FirstIsBottomPt(p, dups)) pp = dups;
		dups = dups->Next;
		while (dups->Pt != pp->Pt) dups = dups->Next;
	    }
	}
	return pp;
    }
    //------------------------------------------------------------------------------

    bool Pt2IsBetweenPt1AndPt3(const IntPoint pt1,
	    const IntPoint pt2, const IntPoint pt3)
    {
	if ((pt1 == pt3) || (pt1 == pt2) || (pt3 == pt2))
	    return false;
	else if (pt1.X != pt3.X)
	    return (pt2.X > pt1.X) == (pt2.X < pt3.X);
	else
	    return (pt2.Y > pt1.Y) == (pt2.Y < pt3.Y);
    }
    //------------------------------------------------------------------------------

    bool HorzSegmentsOverlap(cInt seg1a, cInt seg1b, cInt seg2a, cInt seg2b)
    {
	if (seg1a > seg1b) std::swap(seg1a, seg1b);
	if (seg2a > seg2b) std::swap(seg2a, seg2b);
	return (seg1a < seg2b) && (seg2a < seg1b);
    }

    //------------------------------------------------------------------------------
    // ClipperBase class methods ...
    //------------------------------------------------------------------------------

    ClipperBase::ClipperBase() //constructor
    {
	m_CurrentLM = m_MinimaList.begin(); //begin() == end() here
	m_UseFullRange = false;
    }
    //------------------------------------------------------------------------------

    ClipperBase::~ClipperBase() //destructor
    {
	Clear();
    }
    //------------------------------------------------------------------------------

    void RangeTest(const IntPoint& Pt, bool& useFullRange)
    {
	if (useFullRange)
	{
	    if (Pt.X > hiRange || Pt.Y > hiRange || -Pt.X > hiRange || -Pt.Y > hiRange)
		throw clipperException("Coordinate outside allowed range");
	}
	else if (Pt.X > loRange|| Pt.Y > loRange || -Pt.X > loRange || -Pt.Y > loRange)
	{
	    useFullRange = true;
	    RangeTest(Pt, useFullRange);
	}
    }
    //------------------------------------------------------------------------------

    TEdge* FindNextLocMin(TEdge* E)
    {
	for (;;)
	{
	    while (E->Bot != E->Prev->Bot || E->Curr == E->Top) E = E->Next;
	    if (!IsHorizontal(*E) && !IsHorizontal(*E->Prev)) break;
	    while (IsHorizontal(*E->Prev)) E = E->Prev;
	    TEdge* E2 = E;
	    while (IsHorizontal(*E)) E = E->Next;
	    if (E->Top.Y == E->Prev->Bot.Y) continue; //ie just an intermediate horz.
	    if (E2->Prev->Bot.X < E->Bot.X) E = E2;
	    break;
	}
	return E;
    }
    //------------------------------------------------------------------------------

    TEdge* ClipperBase::ProcessBound(TEdge* E, bool NextIsForward)
    {
	TEdge *Result = E;
	TEdge *Horz = 0;

	if (E->OutIdx == Skip)
	{
	    //if edges still remain in the current bound beyond the skip edge then
	    //create another LocMin and call ProcessBound once more
	    if (NextIsForward)
	    {
		while (E->Top.Y == E->Next->Bot.Y) E = E->Next;
		//don't include top horizontals when parsing a bound a second time,
		//they will be contained in the opposite bound ...
		while (E != Result && IsHorizontal(*E)) E = E->Prev;
	    }
	    else
	    {
		while (E->Top.Y == E->Prev->Bot.Y) E = E->Prev;
		while (E != Result && IsHorizontal(*E)) E = E->Next;
	    }

	    if (E == Result)
	    {
		if (NextIsForward) Result = E->Next;
		else Result = E->Prev;
	    }
	    else
	    {
		//there are more edges in the bound beyond result starting with E
		if (NextIsForward)
		    E = Result->Next;
		else
		    E = Result->Prev;
		MinimaList::value_type locMin;
		locMin.Y = E->Bot.Y;
		locMin.LeftBound = 0;
		locMin.RightBound = E;
		E->WindDelta = 0;
		Result = ProcessBound(E, NextIsForward);
		m_MinimaList.push_back(locMin);
	    }
	    return Result;
	}

	TEdge *EStart;

	if (IsHorizontal(*E))
	{
	    //We need to be careful with open paths because this may not be a
	    //true local minima (ie E may be following a skip edge).
	    //Also, consecutive horz. edges may start heading left before going right.
	    if (NextIsForward)
		EStart = E->Prev;
	    else
		EStart = E->Next;
	    if (IsHorizontal(*EStart)) //ie an adjoining horizontal skip edge
	    {
		if (EStart->Bot.X != E->Bot.X && EStart->Top.X != E->Bot.X)
		    ReverseHorizontal(*E);
	    }
	    else if (EStart->Bot.X != E->Bot.X)
		ReverseHorizontal(*E);
	}

	EStart = E;
	if (NextIsForward)
	{
	    while (Result->Top.Y == Result->Next->Bot.Y && Result->Next->OutIdx != Skip)
		Result = Result->Next;
	    if (IsHorizontal(*Result) && Result->Next->OutIdx != Skip)
	    {
		//nb: at the top of a bound, horizontals are added to the bound
		//only when the preceding edge attaches to the horizontal's left vertex
		//unless a Skip edge is encountered when that becomes the top divide
		Horz = Result;
		while (IsHorizontal(*Horz->Prev)) Horz = Horz->Prev;
		if (Horz->Prev->Top.X > Result->Next->Top.X) Result = Horz->Prev;
	    }
	    while (E != Result)
	    {
		E->NextInLML = E->Next;
		if (IsHorizontal(*E) && E != EStart &&
			E->Bot.X != E->Prev->Top.X) ReverseHorizontal(*E);
		E = E->Next;
	    }
	    if (IsHorizontal(*E) && E != EStart && E->Bot.X != E->Prev->Top.X)
		ReverseHorizontal(*E);
	    Result = Result->Next; //move to the edge just beyond current bound
	} else
	{
	    while (Result->Top.Y == Result->Prev->Bot.Y && Result->Prev->OutIdx != Skip)
		Result = Result->Prev;
	    if (IsHorizontal(*Result) && Result->Prev->OutIdx != Skip)
	    {
		Horz = Result;
		while (IsHorizontal(*Horz->Next)) Horz = Horz->Next;
		if (Horz->Next->Top.X == Result->Prev->Top.X ||
			Horz->Next->Top.X > Result->Prev->Top.X) Result = Horz->Next;
	    }

	    while (E != Result)
	    {
		E->NextInLML = E->Prev;
		if (IsHorizontal(*E) && E != EStart && E->Bot.X != E->Next->Top.X)
		    ReverseHorizontal(*E);
		E = E->Prev;
	    }
	    if (IsHorizontal(*E) && E != EStart && E->Bot.X != E->Next->Top.X)
		ReverseHorizontal(*E);
	    Result = Result->Prev; //move to the edge just beyond current bound
	}

	return Result;
    }
    //------------------------------------------------------------------------------

    bool ClipperBase::AddPath(const Path &pg, PolyType PolyTyp, bool Closed)
    {
#ifdef use_lines
	if (!Closed && PolyTyp == ptClip)
	    throw clipperException("AddPath: Open paths must be subject.");
#else
	if (!Closed)
	    throw clipperException("AddPath: Open paths have been disabled.");
#endif

	int highI = (int)pg.size() -1;
	if (Closed) while (highI > 0 && (pg[highI] == pg[0])) --highI;
	while (highI > 0 && (pg[highI] == pg[highI -1])) --highI;
	if ((Closed && highI < 2) || (!Closed && highI < 1)) return false;

	//create a new edge array ...
	TEdge *edges = new TEdge [highI +1];

	bool IsFlat = true;
	//1. Basic (first) edge initialization ...
	try
	{
	    edges[1].Curr = pg[1];
	    RangeTest(pg[0], m_UseFullRange);
	    RangeTest(pg[highI], m_UseFullRange);
	    InitEdge(&edges[0], &edges[1], &edges[highI], pg[0]);
	    InitEdge(&edges[highI], &edges[0], &edges[highI-1], pg[highI]);
	    for (int i = highI - 1; i >= 1; --i)
	    {
		RangeTest(pg[i], m_UseFullRange);
		InitEdge(&edges[i], &edges[i+1], &edges[i-1], pg[i]);
	    }
	}
	catch(...)
	{
	    delete [] edges;
	    throw; //range test fails
	}
	TEdge *eStart = &edges[0];

	//2. Remove duplicate vertices, and (when closed) collinear edges ...
	TEdge *E = eStart, *eLoopStop = eStart;
	for (;;)
	{
	    //nb: allows matching start and end points when not Closed ...
	    if (E->Curr == E->Next->Curr && (Closed || E->Next != eStart))
	    {
		if (E == E->Next) break;
		if (E == eStart) eStart = E->Next;
		E = RemoveEdge(E);
		eLoopStop = E;
		continue;
	    }
	    if (E->Prev == E->Next)
		break; //only two vertices
	    else if (Closed &&
		    SlopesEqual(E->Prev->Curr, E->Curr, E->Next->Curr, m_UseFullRange) &&
		    (!m_PreserveCollinear ||
		     !Pt2IsBetweenPt1AndPt3(E->Prev->Curr, E->Curr, E->Next->Curr)))
	    {
		//Collinear edges are allowed for open paths but in closed paths
		//the default is to merge adjacent collinear edges into a single edge.
		//However, if the PreserveCollinear property is enabled, only overlapping
		//collinear edges (ie spikes) will be removed from closed paths.
		if (E == eStart) eStart = E->Next;
		E = RemoveEdge(E);
		E = E->Prev;
		eLoopStop = E;
		continue;
	    }
	    E = E->Next;
	    if ((E == eLoopStop) || (!Closed && E->Next == eStart)) break;
	}

	if ((!Closed && (E == E->Next)) || (Closed && (E->Prev == E->Next)))
	{
	    delete [] edges;
	    return false;
	}

	if (!Closed)
	{
	    m_HasOpenPaths = true;
	    eStart->Prev->OutIdx = Skip;
	}

	//3. Do second stage of edge initialization ...
	E = eStart;
	do
	{
	    InitEdge2(*E, PolyTyp);
	    E = E->Next;
	    if (IsFlat && E->Curr.Y != eStart->Curr.Y) IsFlat = false;
	}
	while (E != eStart);

	//4. Finally, add edge bounds to LocalMinima list ...

	//Totally flat paths must be handled differently when adding them
	//to LocalMinima list to avoid endless loops etc ...
	if (IsFlat)
	{
	    if (Closed)
	    {
		delete [] edges;
		return false;
	    }
	    E->Prev->OutIdx = Skip;
	    MinimaList::value_type locMin;
	    locMin.Y = E->Bot.Y;
	    locMin.LeftBound = 0;
	    locMin.RightBound = E;
	    locMin.RightBound->Side = esRight;
	    locMin.RightBound->WindDelta = 0;
	    for (;;)
	    {
		if (E->Bot.X != E->Prev->Top.X) ReverseHorizontal(*E);
		if (E->Next->OutIdx == Skip) break;
		E->NextInLML = E->Next;
		E = E->Next;
	    }
	    m_MinimaList.push_back(locMin);
	    m_edges.push_back(edges);
	    return true;
	}

	m_edges.push_back(edges);
	bool leftBoundIsForward;
	TEdge* EMin = 0;

	//workaround to avoid an endless loop in the while loop below when
	//open paths have matching start and end points ...
	if (E->Prev->Bot == E->Prev->Top) E = E->Next;

	for (;;)
	{
	    E = FindNextLocMin(E);
	    if (E == EMin) break;
	    else if (!EMin) EMin = E;

	    //E and E.Prev now share a local minima (left aligned if horizontal).
	    //Compare their slopes to find which starts which bound ...
	    MinimaList::value_type locMin;
	    locMin.Y = E->Bot.Y;
	    if (E->Dx < E->Prev->Dx)
	    {
		locMin.LeftBound = E->Prev;
		locMin.RightBound = E;
		leftBoundIsForward = false; //Q.nextInLML = Q.prev
	    } else
	    {
		locMin.LeftBound = E;
		locMin.RightBound = E->Prev;
		leftBoundIsForward = true; //Q.nextInLML = Q.next
	    }

	    if (!Closed) locMin.LeftBound->WindDelta = 0;
	    else if (locMin.LeftBound->Next == locMin.RightBound)
		locMin.LeftBound->WindDelta = -1;
	    else locMin.LeftBound->WindDelta = 1;
	    locMin.RightBound->WindDelta = -locMin.LeftBound->WindDelta;

	    E = ProcessBound(locMin.LeftBound, leftBoundIsForward);
	    if (E->OutIdx == Skip) E = ProcessBound(E, leftBoundIsForward);

	    TEdge* E2 = ProcessBound(locMin.RightBound, !leftBoundIsForward);
	    if (E2->OutIdx == Skip) E2 = ProcessBound(E2, !leftBoundIsForward);

	    if (locMin.LeftBound->OutIdx == Skip)
		locMin.LeftBound = 0;
	    else if (locMin.RightBound->OutIdx == Skip)
		locMin.RightBound = 0;
	    m_MinimaList.push_back(locMin);
	    if (!leftBoundIsForward) E = E2;
	}
	return true;
    }
    //------------------------------------------------------------------------------

    bool ClipperBase::AddPaths(const Paths &ppg, PolyType PolyTyp, bool Closed)
    {
	bool result = false;
	for (Paths::size_type i = 0; i < ppg.size(); ++i)
	    if (AddPath(ppg[i], PolyTyp, Closed)) result = true;
	return result;
    }
    //------------------------------------------------------------------------------

    void ClipperBase::Clear()
    {
	DisposeLocalMinimaList();
	for (EdgeList::size_type i = 0; i < m_edges.size(); ++i)
	{
	    TEdge* edges = m_edges[i];
	    delete [] edges;
	}
	m_edges.clear();
	m_UseFullRange = false;
	m_HasOpenPaths = false;
    }
    //------------------------------------------------------------------------------

    void ClipperBase::Reset()
    {
	m_CurrentLM = m_MinimaList.begin();
	if (m_CurrentLM == m_MinimaList.end()) return; //ie nothing to process
	std::sort(m_MinimaList.begin(), m_MinimaList.end(), LocMinSorter());

	m_Scanbeam = ScanbeamList(); //clears/resets priority_queue
	//reset all edges ...
	for (MinimaList::iterator lm = m_MinimaList.begin(); lm != m_MinimaList.end(); ++lm)
	{
	    InsertScanbeam(lm->Y);
	    TEdge* e = lm->LeftBound;
	    if (e)
	    {
		e->Curr = e->Bot;
		e->Side = esLeft;
		e->OutIdx = Unassigned;
	    }

	    e = lm->RightBound;
	    if (e)
	    {
		e->Curr = e->Bot;
		e->Side = esRight;
		e->OutIdx = Unassigned;
	    }
	}
	m_ActiveEdges = 0;
	m_CurrentLM = m_MinimaList.begin();
    }
    //------------------------------------------------------------------------------

    void ClipperBase::DisposeLocalMinimaList()
    {
	m_MinimaList.clear();
	m_CurrentLM = m_MinimaList.begin();
    }
    //------------------------------------------------------------------------------

    bool ClipperBase::PopLocalMinima(cInt Y, const LocalMinimum *&locMin)
    {
	if (m_CurrentLM == m_MinimaList.end() || (*m_CurrentLM).Y != Y) return false;
	locMin = &(*m_CurrentLM);
	++m_CurrentLM;
	return true;
    }
    //------------------------------------------------------------------------------

    IntRect ClipperBase::GetBounds()
    {
	IntRect result;
	MinimaList::iterator lm = m_MinimaList.begin();
	if (lm == m_MinimaList.end())
	{
	    result.left = result.top = result.right = result.bottom = 0;
	    return result;
	}
	result.left = lm->LeftBound->Bot.X;
	result.top = lm->LeftBound->Bot.Y;
	result.right = lm->LeftBound->Bot.X;
	result.bottom = lm->LeftBound->Bot.Y;
	while (lm != m_MinimaList.end())
	{
	    //todo - needs fixing for open paths
	    result.bottom = std::max(result.bottom, lm->LeftBound->Bot.Y);
	    TEdge* e = lm->LeftBound;
	    for (;;) {
		TEdge* bottomE = e;
		while (e->NextInLML)
		{
		    if (e->Bot.X < result.left) result.left = e->Bot.X;
		    if (e->Bot.X > result.right) result.right = e->Bot.X;
		    e = e->NextInLML;
		}
		result.left = std::min(result.left, e->Bot.X);
		result.right = std::max(result.right, e->Bot.X);
		result.left = std::min(result.left, e->Top.X);
		result.right = std::max(result.right, e->Top.X);
		result.top = std::min(result.top, e->Top.Y);
		if (bottomE == lm->LeftBound) e = lm->RightBound;
		else break;
	    }
	    ++lm;
	}
	return result;
    }
    //------------------------------------------------------------------------------

    void ClipperBase::InsertScanbeam(const cInt Y)
    {
	m_Scanbeam.push(Y);
    }
    //------------------------------------------------------------------------------

    bool ClipperBase::PopScanbeam(cInt &Y)
    {
	if (m_Scanbeam.empty()) return false;
	Y = m_Scanbeam.top();
	m_Scanbeam.pop();
	while (!m_Scanbeam.empty() && Y == m_Scanbeam.top()) { m_Scanbeam.pop(); } // Pop duplicates.
	return true;
    }
    //------------------------------------------------------------------------------

    void ClipperBase::DisposeAllOutRecs(){
	for (PolyOutList::size_type i = 0; i < m_PolyOuts.size(); ++i)
	    DisposeOutRec(i);
	m_PolyOuts.clear();
    }
    //------------------------------------------------------------------------------

    void ClipperBase::DisposeOutRec(PolyOutList::size_type index)
    {
	OutRec *outRec = m_PolyOuts[index];
	if (outRec->Pts) DisposeOutPts(outRec->Pts);
	delete outRec;
	m_PolyOuts[index] = 0;
    }
    //------------------------------------------------------------------------------

    void ClipperBase::DeleteFromAEL(TEdge *e)
    {
	TEdge* AelPrev = e->PrevInAEL;
	TEdge* AelNext = e->NextInAEL;
	if (!AelPrev &&  !AelNext && (e != m_ActiveEdges)) return; //already deleted
	if (AelPrev) AelPrev->NextInAEL = AelNext;
	else m_ActiveEdges = AelNext;
	if (AelNext) AelNext->PrevInAEL = AelPrev;
	e->NextInAEL = 0;
	e->PrevInAEL = 0;
    }
    //------------------------------------------------------------------------------

    OutRec* ClipperBase::CreateOutRec()
    {
	OutRec* result = new OutRec;
	result->IsHole = false;
	result->IsOpen = false;
	result->FirstLeft = 0;
	result->Pts = 0;
	result->BottomPt = 0;
	result->PolyNd = 0;
	m_PolyOuts.push_back(result);
	result->Idx = (int)m_PolyOuts.size() - 1;
	return result;
    }
    //------------------------------------------------------------------------------

    void ClipperBase::SwapPositionsInAEL(TEdge *Edge1, TEdge *Edge2)
    {
	//check that one or other edge hasn't already been removed from AEL ...
	if (Edge1->NextInAEL == Edge1->PrevInAEL ||
		Edge2->NextInAEL == Edge2->PrevInAEL) return;

	if (Edge1->NextInAEL == Edge2)
	{
	    TEdge* Next = Edge2->NextInAEL;
	    if (Next) Next->PrevInAEL = Edge1;
	    TEdge* Prev = Edge1->PrevInAEL;
	    if (Prev) Prev->NextInAEL = Edge2;
	    Edge2->PrevInAEL = Prev;
	    Edge2->NextInAEL = Edge1;
	    Edge1->PrevInAEL = Edge2;
	    Edge1->NextInAEL = Next;
	}
	else if (Edge2->NextInAEL == Edge1)
	{
	    TEdge* Next = Edge1->NextInAEL;
	    if (Next) Next->PrevInAEL = Edge2;
	    TEdge* Prev = Edge2->PrevInAEL;
	    if (Prev) Prev->NextInAEL = Edge1;
	    Edge1->PrevInAEL = Prev;
	    Edge1->NextInAEL = Edge2;
	    Edge2->PrevInAEL = Edge1;
	    Edge2->NextInAEL = Next;
	}
	else
	{
	    TEdge* Next = Edge1->NextInAEL;
	    TEdge* Prev = Edge1->PrevInAEL;
	    Edge1->NextInAEL = Edge2->NextInAEL;
	    if (Edge1->NextInAEL) Edge1->NextInAEL->PrevInAEL = Edge1;
	    Edge1->PrevInAEL = Edge2->PrevInAEL;
	    if (Edge1->PrevInAEL) Edge1->PrevInAEL->NextInAEL = Edge1;
	    Edge2->NextInAEL = Next;
	    if (Edge2->NextInAEL) Edge2->NextInAEL->PrevInAEL = Edge2;
	    Edge2->PrevInAEL = Prev;
	    if (Edge2->PrevInAEL) Edge2->PrevInAEL->NextInAEL = Edge2;
	}

	if (!Edge1->PrevInAEL) m_ActiveEdges = Edge1;
	else if (!Edge2->PrevInAEL) m_ActiveEdges = Edge2;
    }
    //------------------------------------------------------------------------------

    void ClipperBase::UpdateEdgeIntoAEL(TEdge *&e)
    {
	if (!e->NextInLML)
	    throw clipperException("UpdateEdgeIntoAEL: invalid call");

	e->NextInLML->OutIdx = e->OutIdx;
	TEdge* AelPrev = e->PrevInAEL;
	TEdge* AelNext = e->NextInAEL;
	if (AelPrev) AelPrev->NextInAEL = e->NextInLML;
	else m_ActiveEdges = e->NextInLML;
	if (AelNext) AelNext->PrevInAEL = e->NextInLML;
	e->NextInLML->Side = e->Side;
	e->NextInLML->WindDelta = e->WindDelta;
	e->NextInLML->WindCnt = e->WindCnt;
	e->NextInLML->WindCnt2 = e->WindCnt2;
	e = e->NextInLML;
	e->Curr = e->Bot;
	e->PrevInAEL = AelPrev;
	e->NextInAEL = AelNext;
	if (!IsHorizontal(*e)) InsertScanbeam(e->Top.Y);
    }
    //------------------------------------------------------------------------------

    bool ClipperBase::LocalMinimaPending()
    {
	return (m_CurrentLM != m_MinimaList.end());
    }

    //------------------------------------------------------------------------------
    // TClipper methods ...
    //------------------------------------------------------------------------------

    Clipper::Clipper(int initOptions) : ClipperBase() //constructor
    {
	m_ExecuteLocked = false;
	m_UseFullRange = false;
	m_ReverseOutput = ((initOptions & ioReverseSolution) != 0);
	m_StrictSimple = ((initOptions & ioStrictlySimple) != 0);
	m_PreserveCollinear = ((initOptions & ioPreserveCollinear) != 0);
	m_HasOpenPaths = false;
#ifdef use_xyz
	m_ZFill = 0;
#endif
    }
    //------------------------------------------------------------------------------

#ifdef use_xyz
    void Clipper::ZFillFunction(ZFillCallback zFillFunc)
    {
	m_ZFill = zFillFunc;
    }
    //------------------------------------------------------------------------------
#endif

    bool Clipper::Execute(ClipType clipType, Paths &solution, PolyFillType fillType)
    {
	return Execute(clipType, solution, fillType, fillType);
    }
    //------------------------------------------------------------------------------

    bool Clipper::Execute(ClipType clipType, PolyTree &polytree, PolyFillType fillType)
    {
	return Execute(clipType, polytree, fillType, fillType);
    }
    //------------------------------------------------------------------------------

    bool Clipper::Execute(ClipType clipType, Paths &solution,
	    PolyFillType subjFillType, PolyFillType clipFillType)
    {
	if( m_ExecuteLocked ) return false;
	if (m_HasOpenPaths)
	    throw clipperException("Error: PolyTree struct is needed for open path clipping.");
	m_ExecuteLocked = true;
	solution.resize(0);
	m_SubjFillType = subjFillType;
	m_ClipFillType = clipFillType;
	m_ClipType = clipType;
	m_UsingPolyTree = false;
	bool succeeded = ExecuteInternal();
	if (succeeded) BuildResult(solution);
	DisposeAllOutRecs();
	m_ExecuteLocked = false;
	return succeeded;
    }
    //------------------------------------------------------------------------------

    bool Clipper::Execute(ClipType clipType, PolyTree& polytree,
	    PolyFillType subjFillType, PolyFillType clipFillType)
    {
	if( m_ExecuteLocked ) return false;
	m_ExecuteLocked = true;
	m_SubjFillType = subjFillType;
	m_ClipFillType = clipFillType;
	m_ClipType = clipType;
	m_UsingPolyTree = true;
	bool succeeded = ExecuteInternal();
	if (succeeded) BuildResult2(polytree);
	DisposeAllOutRecs();
	m_ExecuteLocked = false;
	return succeeded;
    }
    //------------------------------------------------------------------------------

    void Clipper::FixHoleLinkage(OutRec &outrec)
    {
	//skip OutRecs that (a) contain outermost polygons or
	//(b) already have the correct owner/child linkage ...
	if (!outrec.FirstLeft ||
		(outrec.IsHole != outrec.FirstLeft->IsHole &&
		 outrec.FirstLeft->Pts)) return;

	OutRec* orfl = outrec.FirstLeft;
	while (orfl && ((orfl->IsHole == outrec.IsHole) || !orfl->Pts))
	    orfl = orfl->FirstLeft;
	outrec.FirstLeft = orfl;
    }
    //------------------------------------------------------------------------------

    bool Clipper::ExecuteInternal()
    {
	bool succeeded = true;
	try {
	    Reset();
	    m_Maxima = MaximaList();
	    m_SortedEdges = 0;

	    succeeded = true;
	    cInt botY = 0;
	    cInt topY = 0;
	    if (!PopScanbeam(botY)) return false;
	    InsertLocalMinimaIntoAEL(botY);
	    while (PopScanbeam(topY) || LocalMinimaPending())
	    {
		ProcessHorizontals();
		ClearGhostJoins();
		if (!ProcessIntersections(topY))
		{
		    succeeded = false;
		    break;
		}
		ProcessEdgesAtTopOfScanbeam(topY);
		botY = topY;
		InsertLocalMinimaIntoAEL(botY);
	    }
	}
	catch(...)
	{
	    succeeded = false;
	}

	if (succeeded)
	{
	    //fix orientations ...
	    for (PolyOutList::size_type i = 0; i < m_PolyOuts.size(); ++i)
	    {
		OutRec *outRec = m_PolyOuts[i];
		if (!outRec->Pts || outRec->IsOpen) continue;
		if ((outRec->IsHole ^ m_ReverseOutput) == (Area(*outRec) > 0))
		    ReversePolyPtLinks(outRec->Pts);
	    }

	    if (!m_Joins.empty()) JoinCommonEdges();

	    //unfortunately FixupOutPolygon() must be done after JoinCommonEdges()
	    for (PolyOutList::size_type i = 0; i < m_PolyOuts.size(); ++i)
	    {
		OutRec *outRec = m_PolyOuts[i];
		if (!outRec->Pts) continue;
		if (outRec->IsOpen)
		    FixupOutPolyline(*outRec);
		else
		    FixupOutPolygon(*outRec);
	    }

	    if (m_StrictSimple) DoSimplePolygons();
	}

	ClearJoins();
	ClearGhostJoins();
	return succeeded;
    }
    //------------------------------------------------------------------------------

    void Clipper::SetWindingCount(TEdge &edge)
    {
	TEdge *e = edge.PrevInAEL;
	//find the edge of the same polytype that immediately precedes 'edge' in AEL
	while (e  && ((e->PolyTyp != edge.PolyTyp) || (e->WindDelta == 0))) e = e->PrevInAEL;
	if (!e)
	{
	    if (edge.WindDelta == 0)
	    {
		PolyFillType pft = (edge.PolyTyp == ptSubject ? m_SubjFillType : m_ClipFillType);
		edge.WindCnt = (pft == pftNegative ? -1 : 1);
	    }
	    else
		edge.WindCnt = edge.WindDelta;
	    edge.WindCnt2 = 0;
	    e = m_ActiveEdges; //ie get ready to calc WindCnt2
	}
	else if (edge.WindDelta == 0 && m_ClipType != ctUnion)
	{
	    edge.WindCnt = 1;
	    edge.WindCnt2 = e->WindCnt2;
	    e = e->NextInAEL; //ie get ready to calc WindCnt2
	}
	else if (IsEvenOddFillType(edge))
	{
	    //EvenOdd filling ...
	    if (edge.WindDelta == 0)
	    {
		//are we inside a subj polygon ...
		bool Inside = true;
		TEdge *e2 = e->PrevInAEL;
		while (e2)
		{
		    if (e2->PolyTyp == e->PolyTyp && e2->WindDelta != 0)
			Inside = !Inside;
		    e2 = e2->PrevInAEL;
		}
		edge.WindCnt = (Inside ? 0 : 1);
	    }
	    else
	    {
		edge.WindCnt = edge.WindDelta;
	    }
	    edge.WindCnt2 = e->WindCnt2;
	    e = e->NextInAEL; //ie get ready to calc WindCnt2
	}
	else
	{
	    //nonZero, Positive or Negative filling ...
	    if (e->WindCnt * e->WindDelta < 0)
	    {
		//prev edge is 'decreasing' WindCount (WC) toward zero
		//so we're outside the previous polygon ...
		if (Abs(e->WindCnt) > 1)
		{
		    //outside prev poly but still inside another.
		    //when reversing direction of prev poly use the same WC
		    if (e->WindDelta * edge.WindDelta < 0) edge.WindCnt = e->WindCnt;
		    //otherwise continue to 'decrease' WC ...
		    else edge.WindCnt = e->WindCnt + edge.WindDelta;
		}
		else
		    //now outside all polys of same polytype so set own WC ...
		    edge.WindCnt = (edge.WindDelta == 0 ? 1 : edge.WindDelta);
	    } else
	    {
		//prev edge is 'increasing' WindCount (WC) away from zero
		//so we're inside the previous polygon ...
		if (edge.WindDelta == 0)
		    edge.WindCnt = (e->WindCnt < 0 ? e->WindCnt - 1 : e->WindCnt + 1);
		//if wind direction is reversing prev then use same WC
		else if (e->WindDelta * edge.WindDelta < 0) edge.WindCnt = e->WindCnt;
		//otherwise add to WC ...
		else edge.WindCnt = e->WindCnt + edge.WindDelta;
	    }
	    edge.WindCnt2 = e->WindCnt2;
	    e = e->NextInAEL; //ie get ready to calc WindCnt2
	}

	//update WindCnt2 ...
	if (IsEvenOddAltFillType(edge))
	{
	    //EvenOdd filling ...
	    while (e != &edge)
	    {
		if (e->WindDelta != 0)
		    edge.WindCnt2 = (edge.WindCnt2 == 0 ? 1 : 0);
		e = e->NextInAEL;
	    }
	} else
	{
	    //nonZero, Positive or Negative filling ...
	    while ( e != &edge )
	    {
		edge.WindCnt2 += e->WindDelta;
		e = e->NextInAEL;
	    }
	}
    }
    //------------------------------------------------------------------------------

    bool Clipper::IsEvenOddFillType(const TEdge& edge) const
    {
	if (edge.PolyTyp == ptSubject)
	    return m_SubjFillType == pftEvenOdd; else
		return m_ClipFillType == pftEvenOdd;
    }
    //------------------------------------------------------------------------------

    bool Clipper::IsEvenOddAltFillType(const TEdge& edge) const
    {
	if (edge.PolyTyp == ptSubject)
	    return m_ClipFillType == pftEvenOdd; else
		return m_SubjFillType == pftEvenOdd;
    }
    //------------------------------------------------------------------------------

    bool Clipper::IsContributing(const TEdge& edge) const
    {
	PolyFillType pft, pft2;
	if (edge.PolyTyp == ptSubject)
	{
	    pft = m_SubjFillType;
	    pft2 = m_ClipFillType;
	} else
	{
	    pft = m_ClipFillType;
	    pft2 = m_SubjFillType;
	}

	switch(pft)
	{
	    case pftEvenOdd:
		//return false if a subj line has been flagged as inside a subj polygon
		if (edge.WindDelta == 0 && edge.WindCnt != 1) return false;
		break;
	    case pftNonZero:
		if (Abs(edge.WindCnt) != 1) return false;
		break;
	    case pftPositive:
		if (edge.WindCnt != 1) return false;
		break;
	    default: //pftNegative
		if (edge.WindCnt != -1) return false;
	}

	switch(m_ClipType)
	{
	    case ctIntersection:
		switch(pft2)
		{
		    case pftEvenOdd:
		    case pftNonZero:
			return (edge.WindCnt2 != 0);
		    case pftPositive:
			return (edge.WindCnt2 > 0);
		    default:
			return (edge.WindCnt2 < 0);
		}
		break;
	    case ctUnion:
		switch(pft2)
		{
		    case pftEvenOdd:
		    case pftNonZero:
			return (edge.WindCnt2 == 0);
		    case pftPositive:
			return (edge.WindCnt2 <= 0);
		    default:
			return (edge.WindCnt2 >= 0);
		}
		break;
	    case ctDifference:
		if (edge.PolyTyp == ptSubject)
		    switch(pft2)
		    {
			case pftEvenOdd:
			case pftNonZero:
			    return (edge.WindCnt2 == 0);
			case pftPositive:
			    return (edge.WindCnt2 <= 0);
			default:
			    return (edge.WindCnt2 >= 0);
		    }
		else
		    switch(pft2)
		    {
			case pftEvenOdd:
			case pftNonZero:
			    return (edge.WindCnt2 != 0);
			case pftPositive:
			    return (edge.WindCnt2 > 0);
			default:
			    return (edge.WindCnt2 < 0);
		    }
		break;
	    case ctXor:
		if (edge.WindDelta == 0) //XOr always contributing unless open
		    switch(pft2)
		    {
			case pftEvenOdd:
			case pftNonZero:
			    return (edge.WindCnt2 == 0);
			case pftPositive:
			    return (edge.WindCnt2 <= 0);
			default:
			    return (edge.WindCnt2 >= 0);
		    }
		else
		    return true;
		break;
	    default:
		return true;
	}
    }
    //------------------------------------------------------------------------------

    OutPt* Clipper::AddLocalMinPoly(TEdge *e1, TEdge *e2, const IntPoint &Pt)
    {
	OutPt* result;
	TEdge *e, *prevE;
	if (IsHorizontal(*e2) || ( e1->Dx > e2->Dx ))
	{
	    result = AddOutPt(e1, Pt);
	    e2->OutIdx = e1->OutIdx;
	    e1->Side = esLeft;
	    e2->Side = esRight;
	    e = e1;
	    if (e->PrevInAEL == e2)
		prevE = e2->PrevInAEL;
	    else
		prevE = e->PrevInAEL;
	} else
	{
	    result = AddOutPt(e2, Pt);
	    e1->OutIdx = e2->OutIdx;
	    e1->Side = esRight;
	    e2->Side = esLeft;
	    e = e2;
	    if (e->PrevInAEL == e1)
		prevE = e1->PrevInAEL;
	    else
		prevE = e->PrevInAEL;
	}

	if (prevE && prevE->OutIdx >= 0 && prevE->Top.Y < Pt.Y && e->Top.Y < Pt.Y)
	{
	    cInt xPrev = TopX(*prevE, Pt.Y);
	    cInt xE = TopX(*e, Pt.Y);
	    if (xPrev == xE && (e->WindDelta != 0) && (prevE->WindDelta != 0) &&
		    SlopesEqual(IntPoint(xPrev, Pt.Y), prevE->Top, IntPoint(xE, Pt.Y), e->Top, m_UseFullRange))
	    {
		OutPt* outPt = AddOutPt(prevE, Pt);
		AddJoin(result, outPt, e->Top);
	    }
	}
	return result;
    }
    //------------------------------------------------------------------------------

    void Clipper::AddLocalMaxPoly(TEdge *e1, TEdge *e2, const IntPoint &Pt)
    {
	AddOutPt( e1, Pt );
	if (e2->WindDelta == 0) AddOutPt(e2, Pt);
	if( e1->OutIdx == e2->OutIdx )
	{
	    e1->OutIdx = Unassigned;
	    e2->OutIdx = Unassigned;
	}
	else if (e1->OutIdx < e2->OutIdx)
	    AppendPolygon(e1, e2);
	else
	    AppendPolygon(e2, e1);
    }
    //------------------------------------------------------------------------------

    void Clipper::AddEdgeToSEL(TEdge *edge)
    {
	//SEL pointers in PEdge are reused to build a list of horizontal edges.
	//However, we don't need to worry about order with horizontal edge processing.
	if( !m_SortedEdges )
	{
	    m_SortedEdges = edge;
	    edge->PrevInSEL = 0;
	    edge->NextInSEL = 0;
	}
	else
	{
	    edge->NextInSEL = m_SortedEdges;
	    edge->PrevInSEL = 0;
	    m_SortedEdges->PrevInSEL = edge;
	    m_SortedEdges = edge;
	}
    }
    //------------------------------------------------------------------------------

    bool Clipper::PopEdgeFromSEL(TEdge *&edge)
    {
	if (!m_SortedEdges) return false;
	edge = m_SortedEdges;
	DeleteFromSEL(m_SortedEdges);
	return true;
    }
    //------------------------------------------------------------------------------

    void Clipper::CopyAELToSEL()
    {
	TEdge* e = m_ActiveEdges;
	m_SortedEdges = e;
	while ( e )
	{
	    e->PrevInSEL = e->PrevInAEL;
	    e->NextInSEL = e->NextInAEL;
	    e = e->NextInAEL;
	}
    }
    //------------------------------------------------------------------------------

    void Clipper::AddJoin(OutPt *op1, OutPt *op2, const IntPoint OffPt)
    {
	Join* j = new Join;
	j->OutPt1 = op1;
	j->OutPt2 = op2;
	j->OffPt = OffPt;
	m_Joins.push_back(j);
    }
    //------------------------------------------------------------------------------

    void Clipper::ClearJoins()
    {
	for (JoinList::size_type i = 0; i < m_Joins.size(); i++)
	    delete m_Joins[i];
	m_Joins.resize(0);
    }
    //------------------------------------------------------------------------------

    void Clipper::ClearGhostJoins()
    {
	for (JoinList::size_type i = 0; i < m_GhostJoins.size(); i++)
	    delete m_GhostJoins[i];
	m_GhostJoins.resize(0);
    }
    //------------------------------------------------------------------------------

    void Clipper::AddGhostJoin(OutPt *op, const IntPoint OffPt)
    {
	Join* j = new Join;
	j->OutPt1 = op;
	j->OutPt2 = 0;
	j->OffPt = OffPt;
	m_GhostJoins.push_back(j);
    }
    //------------------------------------------------------------------------------

    void Clipper::InsertLocalMinimaIntoAEL(const cInt botY)
    {
	const LocalMinimum *lm;
	while (PopLocalMinima(botY, lm))
	{
	    TEdge* lb = lm->LeftBound;
	    TEdge* rb = lm->RightBound;

	    OutPt *Op1 = 0;
	    if (!lb)
	    {
		//nb: don't insert LB into either AEL or SEL
		InsertEdgeIntoAEL(rb, 0);
		SetWindingCount(*rb);
		if (IsContributing(*rb))
		    Op1 = AddOutPt(rb, rb->Bot);
	    }
	    else if (!rb)
	    {
		InsertEdgeIntoAEL(lb, 0);
		SetWindingCount(*lb);
		if (IsContributing(*lb))
		    Op1 = AddOutPt(lb, lb->Bot);
		InsertScanbeam(lb->Top.Y);
	    }
	    else
	    {
		InsertEdgeIntoAEL(lb, 0);
		InsertEdgeIntoAEL(rb, lb);
		SetWindingCount( *lb );
		rb->WindCnt = lb->WindCnt;
		rb->WindCnt2 = lb->WindCnt2;
		if (IsContributing(*lb))
		    Op1 = AddLocalMinPoly(lb, rb, lb->Bot);
		InsertScanbeam(lb->Top.Y);
	    }

	    if (rb)
	    {
		if (IsHorizontal(*rb))
		{
		    AddEdgeToSEL(rb);
		    if (rb->NextInLML)
			InsertScanbeam(rb->NextInLML->Top.Y);
		}
		else InsertScanbeam( rb->Top.Y );
	    }

	    if (!lb || !rb) continue;

	    //if any output polygons share an edge, they'll need joining later ...
	    if (Op1 && IsHorizontal(*rb) &&
		    m_GhostJoins.size() > 0 && (rb->WindDelta != 0))
	    {
		for (JoinList::size_type i = 0; i < m_GhostJoins.size(); ++i)
		{
		    Join* jr = m_GhostJoins[i];
		    //if the horizontal Rb and a 'ghost' horizontal overlap, then convert
		    //the 'ghost' join to a real join ready for later ...
		    if (HorzSegmentsOverlap(jr->OutPt1->Pt.X, jr->OffPt.X, rb->Bot.X, rb->Top.X))
			AddJoin(jr->OutPt1, Op1, jr->OffPt);
		}
	    }

	    if (lb->OutIdx >= 0 && lb->PrevInAEL &&
		    lb->PrevInAEL->Curr.X == lb->Bot.X &&
		    lb->PrevInAEL->OutIdx >= 0 &&
		    SlopesEqual(lb->PrevInAEL->Bot, lb->PrevInAEL->Top, lb->Curr, lb->Top, m_UseFullRange) &&
		    (lb->WindDelta != 0) && (lb->PrevInAEL->WindDelta != 0))
	    {
		OutPt *Op2 = AddOutPt(lb->PrevInAEL, lb->Bot);
		AddJoin(Op1, Op2, lb->Top);
	    }

	    if(lb->NextInAEL != rb)
	    {

		if (rb->OutIdx >= 0 && rb->PrevInAEL->OutIdx >= 0 &&
			SlopesEqual(rb->PrevInAEL->Curr, rb->PrevInAEL->Top, rb->Curr, rb->Top, m_UseFullRange) &&
			(rb->WindDelta != 0) && (rb->PrevInAEL->WindDelta != 0))
		{
		    OutPt *Op2 = AddOutPt(rb->PrevInAEL, rb->Bot);
		    AddJoin(Op1, Op2, rb->Top);
		}

		TEdge* e = lb->NextInAEL;
		if (e)
		{
		    while( e != rb )
		    {
			//nb: For calculating winding counts etc, IntersectEdges() assumes
			//that param1 will be to the Right of param2 ABOVE the intersection ...
			IntersectEdges(rb , e , lb->Curr); //order important here
			e = e->NextInAEL;
		    }
		}
	    }

	}
    }
    //------------------------------------------------------------------------------

    void Clipper::DeleteFromSEL(TEdge *e)
    {
	TEdge* SelPrev = e->PrevInSEL;
	TEdge* SelNext = e->NextInSEL;
	if( !SelPrev &&  !SelNext && (e != m_SortedEdges) ) return; //already deleted
	if( SelPrev ) SelPrev->NextInSEL = SelNext;
	else m_SortedEdges = SelNext;
	if( SelNext ) SelNext->PrevInSEL = SelPrev;
	e->NextInSEL = 0;
	e->PrevInSEL = 0;
    }
    //------------------------------------------------------------------------------

#ifdef use_xyz
    void Clipper::SetZ(IntPoint& pt, TEdge& e1, TEdge& e2)
    {
	if (pt.Z != 0 || !m_ZFill) return;
	else if (pt == e1.Bot) pt.Z = e1.Bot.Z;
	else if (pt == e1.Top) pt.Z = e1.Top.Z;
	else if (pt == e2.Bot) pt.Z = e2.Bot.Z;
	else if (pt == e2.Top) pt.Z = e2.Top.Z;
	else (*m_ZFill)(e1.Bot, e1.Top, e2.Bot, e2.Top, pt);
    }
    //------------------------------------------------------------------------------
#endif

    void Clipper::IntersectEdges(TEdge *e1, TEdge *e2, IntPoint &Pt)
    {
	bool e1Contributing = ( e1->OutIdx >= 0 );
	bool e2Contributing = ( e2->OutIdx >= 0 );

#ifdef use_xyz
	SetZ(Pt, *e1, *e2);
#endif

#ifdef use_lines
	//if either edge is on an OPEN path ...
	if (e1->WindDelta == 0 || e2->WindDelta == 0)
	{
	    //ignore subject-subject open path intersections UNLESS they
	    //are both open paths, AND they are both 'contributing maximas' ...
	    if (e1->WindDelta == 0 && e2->WindDelta == 0) return;

	    //if intersecting a subj line with a subj poly ...
	    else if (e1->PolyTyp == e2->PolyTyp &&
		    e1->WindDelta != e2->WindDelta && m_ClipType == ctUnion)
	    {
		if (e1->WindDelta == 0)
		{
		    if (e2Contributing)
		    {
			AddOutPt(e1, Pt);
			if (e1Contributing) e1->OutIdx = Unassigned;
		    }
		}
		else
		{
		    if (e1Contributing)
		    {
			AddOutPt(e2, Pt);
			if (e2Contributing) e2->OutIdx = Unassigned;
		    }
		}
	    }
	    else if (e1->PolyTyp != e2->PolyTyp)
	    {
		//toggle subj open path OutIdx on/off when Abs(clip.WndCnt) == 1 ...
		if ((e1->WindDelta == 0) && abs(e2->WindCnt) == 1 &&
			(m_ClipType != ctUnion || e2->WindCnt2 == 0))
		{
		    AddOutPt(e1, Pt);
		    if (e1Contributing) e1->OutIdx = Unassigned;
		}
		else if ((e2->WindDelta == 0) && (abs(e1->WindCnt) == 1) &&
			(m_ClipType != ctUnion || e1->WindCnt2 == 0))
		{
		    AddOutPt(e2, Pt);
		    if (e2Contributing) e2->OutIdx = Unassigned;
		}
	    }
	    return;
	}
#endif

	//update winding counts...
	//assumes that e1 will be to the Right of e2 ABOVE the intersection
	if ( e1->PolyTyp == e2->PolyTyp )
	{
	    if ( IsEvenOddFillType( *e1) )
	    {
		int oldE1WindCnt = e1->WindCnt;
		e1->WindCnt = e2->WindCnt;
		e2->WindCnt = oldE1WindCnt;
	    } else
	    {
		if (e1->WindCnt + e2->WindDelta == 0 ) e1->WindCnt = -e1->WindCnt;
		else e1->WindCnt += e2->WindDelta;
		if ( e2->WindCnt - e1->WindDelta == 0 ) e2->WindCnt = -e2->WindCnt;
		else e2->WindCnt -= e1->WindDelta;
	    }
	} else
	{
	    if (!IsEvenOddFillType(*e2)) e1->WindCnt2 += e2->WindDelta;
	    else e1->WindCnt2 = ( e1->WindCnt2 == 0 ) ? 1 : 0;
	    if (!IsEvenOddFillType(*e1)) e2->WindCnt2 -= e1->WindDelta;
	    else e2->WindCnt2 = ( e2->WindCnt2 == 0 ) ? 1 : 0;
	}

	PolyFillType e1FillType, e2FillType, e1FillType2, e2FillType2;
	if (e1->PolyTyp == ptSubject)
	{
	    e1FillType = m_SubjFillType;
	    e1FillType2 = m_ClipFillType;
	} else
	{
	    e1FillType = m_ClipFillType;
	    e1FillType2 = m_SubjFillType;
	}
	if (e2->PolyTyp == ptSubject)
	{
	    e2FillType = m_SubjFillType;
	    e2FillType2 = m_ClipFillType;
	} else
	{
	    e2FillType = m_ClipFillType;
	    e2FillType2 = m_SubjFillType;
	}

	cInt e1Wc, e2Wc;
	switch (e1FillType)
	{
	    case pftPositive: e1Wc = e1->WindCnt; break;
	    case pftNegative: e1Wc = -e1->WindCnt; break;
	    default: e1Wc = Abs(e1->WindCnt);
	}
	switch(e2FillType)
	{
	    case pftPositive: e2Wc = e2->WindCnt; break;
	    case pftNegative: e2Wc = -e2->WindCnt; break;
	    default: e2Wc = Abs(e2->WindCnt);
	}

	if ( e1Contributing && e2Contributing )
	{
	    if ((e1Wc != 0 && e1Wc != 1) || (e2Wc != 0 && e2Wc != 1) ||
		    (e1->PolyTyp != e2->PolyTyp && m_ClipType != ctXor) )
	    {
		AddLocalMaxPoly(e1, e2, Pt);
	    }
	    else
	    {
		AddOutPt(e1, Pt);
		AddOutPt(e2, Pt);
		SwapSides( *e1 , *e2 );
		SwapPolyIndexes( *e1 , *e2 );
	    }
	}
	else if ( e1Contributing )
	{
	    if (e2Wc == 0 || e2Wc == 1)
	    {
		AddOutPt(e1, Pt);
		SwapSides(*e1, *e2);
		SwapPolyIndexes(*e1, *e2);
	    }
	}
	else if ( e2Contributing )
	{
	    if (e1Wc == 0 || e1Wc == 1)
	    {
		AddOutPt(e2, Pt);
		SwapSides(*e1, *e2);
		SwapPolyIndexes(*e1, *e2);
	    }
	}
	else if ( (e1Wc == 0 || e1Wc == 1) && (e2Wc == 0 || e2Wc == 1))
	{
	    //neither edge is currently contributing ...

	    cInt e1Wc2, e2Wc2;
	    switch (e1FillType2)
	    {
		case pftPositive: e1Wc2 = e1->WindCnt2; break;
		case pftNegative : e1Wc2 = -e1->WindCnt2; break;
		default: e1Wc2 = Abs(e1->WindCnt2);
	    }
	    switch (e2FillType2)
	    {
		case pftPositive: e2Wc2 = e2->WindCnt2; break;
		case pftNegative: e2Wc2 = -e2->WindCnt2; break;
		default: e2Wc2 = Abs(e2->WindCnt2);
	    }

	    if (e1->PolyTyp != e2->PolyTyp)
	    {
		AddLocalMinPoly(e1, e2, Pt);
	    }
	    else if (e1Wc == 1 && e2Wc == 1)
		switch( m_ClipType ) {
		    case ctIntersection:
			if (e1Wc2 > 0 && e2Wc2 > 0)
			    AddLocalMinPoly(e1, e2, Pt);
			break;
		    case ctUnion:
			if ( e1Wc2 <= 0 && e2Wc2 <= 0 )
			    AddLocalMinPoly(e1, e2, Pt);
			break;
		    case ctDifference:
			if (((e1->PolyTyp == ptClip) && (e1Wc2 > 0) && (e2Wc2 > 0)) ||
				((e1->PolyTyp == ptSubject) && (e1Wc2 <= 0) && (e2Wc2 <= 0)))
			    AddLocalMinPoly(e1, e2, Pt);
			break;
		    case ctXor:
			AddLocalMinPoly(e1, e2, Pt);
		}
	    else
		SwapSides( *e1, *e2 );
	}
    }
    //------------------------------------------------------------------------------

    void Clipper::SetHoleState(TEdge *e, OutRec *outrec)
    {
	TEdge *e2 = e->PrevInAEL;
	TEdge *eTmp = 0;
	while (e2)
	{
	    if (e2->OutIdx >= 0 && e2->WindDelta != 0)
	    {
		if (!eTmp) eTmp = e2;
		else if (eTmp->OutIdx == e2->OutIdx) eTmp = 0;
	    }
	    e2 = e2->PrevInAEL;
	}
	if (!eTmp)
	{
	    outrec->FirstLeft = 0;
	    outrec->IsHole = false;
	}
	else
	{
	    outrec->FirstLeft = m_PolyOuts[eTmp->OutIdx];
	    outrec->IsHole = !outrec->FirstLeft->IsHole;
	}
    }
    //------------------------------------------------------------------------------

    OutRec* GetLowermostRec(OutRec *outRec1, OutRec *outRec2)
    {
	//work out which polygon fragment has the correct hole state ...
	if (!outRec1->BottomPt)
	    outRec1->BottomPt = GetBottomPt(outRec1->Pts);
	if (!outRec2->BottomPt)
	    outRec2->BottomPt = GetBottomPt(outRec2->Pts);
	OutPt *OutPt1 = outRec1->BottomPt;
	OutPt *OutPt2 = outRec2->BottomPt;
	if (OutPt1->Pt.Y > OutPt2->Pt.Y) return outRec1;
	else if (OutPt1->Pt.Y < OutPt2->Pt.Y) return outRec2;
	else if (OutPt1->Pt.X < OutPt2->Pt.X) return outRec1;
	else if (OutPt1->Pt.X > OutPt2->Pt.X) return outRec2;
	else if (OutPt1->Next == OutPt1) return outRec2;
	else if (OutPt2->Next == OutPt2) return outRec1;
	else if (FirstIsBottomPt(OutPt1, OutPt2)) return outRec1;
	else return outRec2;
    }
    //------------------------------------------------------------------------------

    bool OutRec1RightOfOutRec2(OutRec* outRec1, OutRec* outRec2)
    {
	do
	{
	    outRec1 = outRec1->FirstLeft;
	    if (outRec1 == outRec2) return true;
	} while (outRec1);
	return false;
    }
    //------------------------------------------------------------------------------

    OutRec* Clipper::GetOutRec(int Idx)
    {
	OutRec* outrec = m_PolyOuts[Idx];
	while (outrec != m_PolyOuts[outrec->Idx])
	    outrec = m_PolyOuts[outrec->Idx];
	return outrec;
    }
    //------------------------------------------------------------------------------

    void Clipper::AppendPolygon(TEdge *e1, TEdge *e2)
    {
	//get the start and ends of both output polygons ...
	OutRec *outRec1 = m_PolyOuts[e1->OutIdx];
	OutRec *outRec2 = m_PolyOuts[e2->OutIdx];

	OutRec *holeStateRec;
	if (OutRec1RightOfOutRec2(outRec1, outRec2))
	    holeStateRec = outRec2;
	else if (OutRec1RightOfOutRec2(outRec2, outRec1))
	    holeStateRec = outRec1;
	else
	    holeStateRec = GetLowermostRec(outRec1, outRec2);

	//get the start and ends of both output polygons and
	//join e2 poly onto e1 poly and delete pointers to e2 ...

	OutPt* p1_lft = outRec1->Pts;
	OutPt* p1_rt = p1_lft->Prev;
	OutPt* p2_lft = outRec2->Pts;
	OutPt* p2_rt = p2_lft->Prev;

	//join e2 poly onto e1 poly and delete pointers to e2 ...
	if(  e1->Side == esLeft )
	{
	    if(  e2->Side == esLeft )
	    {
		//z y x a b c
		ReversePolyPtLinks(p2_lft);
		p2_lft->Next = p1_lft;
		p1_lft->Prev = p2_lft;
		p1_rt->Next = p2_rt;
		p2_rt->Prev = p1_rt;
		outRec1->Pts = p2_rt;
	    } else
	    {
		//x y z a b c
		p2_rt->Next = p1_lft;
		p1_lft->Prev = p2_rt;
		p2_lft->Prev = p1_rt;
		p1_rt->Next = p2_lft;
		outRec1->Pts = p2_lft;
	    }
	} else
	{
	    if(  e2->Side == esRight )
	    {
		//a b c z y x
		ReversePolyPtLinks(p2_lft);
		p1_rt->Next = p2_rt;
		p2_rt->Prev = p1_rt;
		p2_lft->Next = p1_lft;
		p1_lft->Prev = p2_lft;
	    } else
	    {
		//a b c x y z
		p1_rt->Next = p2_lft;
		p2_lft->Prev = p1_rt;
		p1_lft->Prev = p2_rt;
		p2_rt->Next = p1_lft;
	    }
	}

	outRec1->BottomPt = 0;
	if (holeStateRec == outRec2)
	{
	    if (outRec2->FirstLeft != outRec1)
		outRec1->FirstLeft = outRec2->FirstLeft;
	    outRec1->IsHole = outRec2->IsHole;
	}
	outRec2->Pts = 0;
	outRec2->BottomPt = 0;
	outRec2->FirstLeft = outRec1;

	int OKIdx = e1->OutIdx;
	int ObsoleteIdx = e2->OutIdx;

	e1->OutIdx = Unassigned; //nb: safe because we only get here via AddLocalMaxPoly
	e2->OutIdx = Unassigned;

	TEdge* e = m_ActiveEdges;
	while( e )
	{
	    if( e->OutIdx == ObsoleteIdx )
	    {
		e->OutIdx = OKIdx;
		e->Side = e1->Side;
		break;
	    }
	    e = e->NextInAEL;
	}

	outRec2->Idx = outRec1->Idx;
    }
    //------------------------------------------------------------------------------

    OutPt* Clipper::AddOutPt(TEdge *e, const IntPoint &pt)
    {
	if(  e->OutIdx < 0 )
	{
	    OutRec *outRec = CreateOutRec();
	    outRec->IsOpen = (e->WindDelta == 0);
	    OutPt* newOp = new OutPt;
	    outRec->Pts = newOp;
	    newOp->Idx = outRec->Idx;
	    newOp->Pt = pt;
	    newOp->Next = newOp;
	    newOp->Prev = newOp;
	    if (!outRec->IsOpen)
		SetHoleState(e, outRec);
	    e->OutIdx = outRec->Idx;
	    return newOp;
	} else
	{
	    OutRec *outRec = m_PolyOuts[e->OutIdx];
	    //OutRec.Pts is the 'Left-most' point & OutRec.Pts.Prev is the 'Right-most'
	    OutPt* op = outRec->Pts;

	    bool ToFront = (e->Side == esLeft);
	    if (ToFront && (pt == op->Pt)) return op;
	    else if (!ToFront && (pt == op->Prev->Pt)) return op->Prev;

	    OutPt* newOp = new OutPt;
	    newOp->Idx = outRec->Idx;
	    newOp->Pt = pt;
	    newOp->Next = op;
	    newOp->Prev = op->Prev;
	    newOp->Prev->Next = newOp;
	    op->Prev = newOp;
	    if (ToFront) outRec->Pts = newOp;
	    return newOp;
	}
    }
    //------------------------------------------------------------------------------

    OutPt* Clipper::GetLastOutPt(TEdge *e)
    {
	OutRec *outRec = m_PolyOuts[e->OutIdx];
	if (e->Side == esLeft)
	    return outRec->Pts;
	else
	    return outRec->Pts->Prev;
    }
    //------------------------------------------------------------------------------

    void Clipper::ProcessHorizontals()
    {
	TEdge* horzEdge;
	while (PopEdgeFromSEL(horzEdge))
	    ProcessHorizontal(horzEdge);
    }
    //------------------------------------------------------------------------------

    inline bool IsMinima(TEdge *e)
    {
	return e  && (e->Prev->NextInLML != e) && (e->Next->NextInLML != e);
    }
    //------------------------------------------------------------------------------

    inline bool IsMaxima(TEdge *e, const cInt Y)
    {
	return e && e->Top.Y == Y && !e->NextInLML;
    }
    //------------------------------------------------------------------------------

    inline bool IsIntermediate(TEdge *e, const cInt Y)
    {
	return e->Top.Y == Y && e->NextInLML;
    }
    //------------------------------------------------------------------------------

    TEdge *GetMaximaPair(TEdge *e)
    {
	if ((e->Next->Top == e->Top) && !e->Next->NextInLML)
	    return e->Next;
	else if ((e->Prev->Top == e->Top) && !e->Prev->NextInLML)
	    return e->Prev;
	else return 0;
    }
    //------------------------------------------------------------------------------

    TEdge *GetMaximaPairEx(TEdge *e)
    {
	//as GetMaximaPair() but returns 0 if MaxPair isn't in AEL (unless it's horizontal)
	TEdge* result = GetMaximaPair(e);
	if (result && (result->OutIdx == Skip ||
		    (result->NextInAEL == result->PrevInAEL && !IsHorizontal(*result)))) return 0;
	return result;
    }
    //------------------------------------------------------------------------------

    void Clipper::SwapPositionsInSEL(TEdge *Edge1, TEdge *Edge2)
    {
	if(  !( Edge1->NextInSEL ) &&  !( Edge1->PrevInSEL ) ) return;
	if(  !( Edge2->NextInSEL ) &&  !( Edge2->PrevInSEL ) ) return;

	if(  Edge1->NextInSEL == Edge2 )
	{
	    TEdge* Next = Edge2->NextInSEL;
	    if( Next ) Next->PrevInSEL = Edge1;
	    TEdge* Prev = Edge1->PrevInSEL;
	    if( Prev ) Prev->NextInSEL = Edge2;
	    Edge2->PrevInSEL = Prev;
	    Edge2->NextInSEL = Edge1;
	    Edge1->PrevInSEL = Edge2;
	    Edge1->NextInSEL = Next;
	}
	else if(  Edge2->NextInSEL == Edge1 )
	{
	    TEdge* Next = Edge1->NextInSEL;
	    if( Next ) Next->PrevInSEL = Edge2;
	    TEdge* Prev = Edge2->PrevInSEL;
	    if( Prev ) Prev->NextInSEL = Edge1;
	    Edge1->PrevInSEL = Prev;
	    Edge1->NextInSEL = Edge2;
	    Edge2->PrevInSEL = Edge1;
	    Edge2->NextInSEL = Next;
	}
	else
	{
	    TEdge* Next = Edge1->NextInSEL;
	    TEdge* Prev = Edge1->PrevInSEL;
	    Edge1->NextInSEL = Edge2->NextInSEL;
	    if( Edge1->NextInSEL ) Edge1->NextInSEL->PrevInSEL = Edge1;
	    Edge1->PrevInSEL = Edge2->PrevInSEL;
	    if( Edge1->PrevInSEL ) Edge1->PrevInSEL->NextInSEL = Edge1;
	    Edge2->NextInSEL = Next;
	    if( Edge2->NextInSEL ) Edge2->NextInSEL->PrevInSEL = Edge2;
	    Edge2->PrevInSEL = Prev;
	    if( Edge2->PrevInSEL ) Edge2->PrevInSEL->NextInSEL = Edge2;
	}

	if( !Edge1->PrevInSEL ) m_SortedEdges = Edge1;
	else if( !Edge2->PrevInSEL ) m_SortedEdges = Edge2;
    }
    //------------------------------------------------------------------------------

    TEdge* GetNextInAEL(TEdge *e, Direction dir)
    {
	return dir == dLeftToRight ? e->NextInAEL : e->PrevInAEL;
    }
    //------------------------------------------------------------------------------

    void GetHorzDirection(TEdge& HorzEdge, Direction& Dir, cInt& Left, cInt& Right)
    {
	if (HorzEdge.Bot.X < HorzEdge.Top.X)
	{
	    Left = HorzEdge.Bot.X;
	    Right = HorzEdge.Top.X;
	    Dir = dLeftToRight;
	} else
	{
	    Left = HorzEdge.Top.X;
	    Right = HorzEdge.Bot.X;
	    Dir = dRightToLeft;
	}
    }
    //------------------------------------------------------------------------

    /*******************************************************************************
     * Notes: Horizontal edges (HEs) at scanline intersections (ie at the Top or    *
     * Bottom of a scanbeam) are processed as if layered. The order in which HEs    *
     * are processed doesn't matter. HEs intersect with other HE Bot.Xs only [#]    *
     * (or they could intersect with Top.Xs only, ie EITHER Bot.Xs OR Top.Xs),      *
     * and with other non-horizontal edges [*]. Once these intersections are        *
     * processed, intermediate HEs then 'promote' the Edge above (NextInLML) into   *
     * the AEL. These 'promoted' edges may in turn intersect [%] with other HEs.    *
     *******************************************************************************/

    void Clipper::ProcessHorizontal(TEdge *horzEdge)
    {
	Direction dir;
	cInt horzLeft, horzRight;
	bool IsOpen = (horzEdge->WindDelta == 0);

	GetHorzDirection(*horzEdge, dir, horzLeft, horzRight);

	TEdge* eLastHorz = horzEdge, *eMaxPair = 0;
	while (eLastHorz->NextInLML && IsHorizontal(*eLastHorz->NextInLML))
	    eLastHorz = eLastHorz->NextInLML;
	if (!eLastHorz->NextInLML)
	    eMaxPair = GetMaximaPair(eLastHorz);

	MaximaList::const_iterator maxIt;
	MaximaList::const_reverse_iterator maxRit;
	if (m_Maxima.size() > 0)
	{
	    //get the first maxima in range (X) ...
	    if (dir == dLeftToRight)
	    {
		maxIt = m_Maxima.begin();
		while (maxIt != m_Maxima.end() && *maxIt <= horzEdge->Bot.X) maxIt++;
		if (maxIt != m_Maxima.end() && *maxIt >= eLastHorz->Top.X)
		    maxIt = m_Maxima.end();
	    }
	    else
	    {
		maxRit = m_Maxima.rbegin();
		while (maxRit != m_Maxima.rend() && *maxRit > horzEdge->Bot.X) maxRit++;
		if (maxRit != m_Maxima.rend() && *maxRit <= eLastHorz->Top.X)
		    maxRit = m_Maxima.rend();
	    }
	}

	OutPt* op1 = 0;

	for (;;) //loop through consec. horizontal edges
	{

	    bool IsLastHorz = (horzEdge == eLastHorz);
	    TEdge* e = GetNextInAEL(horzEdge, dir);
	    while(e)
	    {

		//this code block inserts extra coords into horizontal edges (in output
		//polygons) wherever maxima touch these horizontal edges. This helps
		//'simplifying' polygons (ie if the Simplify property is set).
		if (m_Maxima.size() > 0)
		{
		    if (dir == dLeftToRight)
		    {
			while (maxIt != m_Maxima.end() && *maxIt < e->Curr.X)
			{
			    if (horzEdge->OutIdx >= 0 && !IsOpen)
				AddOutPt(horzEdge, IntPoint(*maxIt, horzEdge->Bot.Y));
			    maxIt++;
			}
		    }
		    else
		    {
			while (maxRit != m_Maxima.rend() && *maxRit > e->Curr.X)
			{
			    if (horzEdge->OutIdx >= 0 && !IsOpen)
				AddOutPt(horzEdge, IntPoint(*maxRit, horzEdge->Bot.Y));
			    maxRit++;
			}
		    }
		};

		if ((dir == dLeftToRight && e->Curr.X > horzRight) ||
			(dir == dRightToLeft && e->Curr.X < horzLeft)) break;

		//Also break if we've got to the end of an intermediate horizontal edge ...
		//nb: Smaller Dx's are to the right of larger Dx's ABOVE the horizontal.
		if (e->Curr.X == horzEdge->Top.X && horzEdge->NextInLML &&
			e->Dx < horzEdge->NextInLML->Dx) break;

		if (horzEdge->OutIdx >= 0 && !IsOpen)  //note: may be done multiple times
		{
#ifdef use_xyz
		    if (dir == dLeftToRight) SetZ(e->Curr, *horzEdge, *e);
		    else SetZ(e->Curr, *e, *horzEdge);
#endif
		    op1 = AddOutPt(horzEdge, e->Curr);
		    TEdge* eNextHorz = m_SortedEdges;
		    while (eNextHorz)
		    {
			if (eNextHorz->OutIdx >= 0 &&
				HorzSegmentsOverlap(horzEdge->Bot.X,
				    horzEdge->Top.X, eNextHorz->Bot.X, eNextHorz->Top.X))
			{
			    OutPt* op2 = GetLastOutPt(eNextHorz);
			    AddJoin(op2, op1, eNextHorz->Top);
			}
			eNextHorz = eNextHorz->NextInSEL;
		    }
		    AddGhostJoin(op1, horzEdge->Bot);
		}

		//OK, so far we're still in range of the horizontal Edge  but make sure
		//we're at the last of consec. horizontals when matching with eMaxPair
		if(e == eMaxPair && IsLastHorz)
		{
		    if (horzEdge->OutIdx >= 0)
			AddLocalMaxPoly(horzEdge, eMaxPair, horzEdge->Top);
		    DeleteFromAEL(horzEdge);
		    DeleteFromAEL(eMaxPair);
		    return;
		}

		if(dir == dLeftToRight)
		{
		    IntPoint Pt = IntPoint(e->Curr.X, horzEdge->Curr.Y);
		    IntersectEdges(horzEdge, e, Pt);
		}
		else
		{
		    IntPoint Pt = IntPoint(e->Curr.X, horzEdge->Curr.Y);
		    IntersectEdges( e, horzEdge, Pt);
		}
		TEdge* eNext = GetNextInAEL(e, dir);
		SwapPositionsInAEL( horzEdge, e );
		e = eNext;
	    } //end while(e)

	    //Break out of loop if HorzEdge.NextInLML is not also horizontal ...
	    if (!horzEdge->NextInLML || !IsHorizontal(*horzEdge->NextInLML)) break;

	    UpdateEdgeIntoAEL(horzEdge);
	    if (horzEdge->OutIdx >= 0) AddOutPt(horzEdge, horzEdge->Bot);
	    GetHorzDirection(*horzEdge, dir, horzLeft, horzRight);

	} //end for (;;)

	if (horzEdge->OutIdx >= 0 && !op1)
	{
	    op1 = GetLastOutPt(horzEdge);
	    TEdge* eNextHorz = m_SortedEdges;
	    while (eNextHorz)
	    {
		if (eNextHorz->OutIdx >= 0 &&
			HorzSegmentsOverlap(horzEdge->Bot.X,
			    horzEdge->Top.X, eNextHorz->Bot.X, eNextHorz->Top.X))
		{
		    OutPt* op2 = GetLastOutPt(eNextHorz);
		    AddJoin(op2, op1, eNextHorz->Top);
		}
		eNextHorz = eNextHorz->NextInSEL;
	    }
	    AddGhostJoin(op1, horzEdge->Top);
	}

	if (horzEdge->NextInLML)
	{
	    if(horzEdge->OutIdx >= 0)
	    {
		op1 = AddOutPt( horzEdge, horzEdge->Top);
		UpdateEdgeIntoAEL(horzEdge);
		if (horzEdge->WindDelta == 0) return;
		//nb: HorzEdge is no longer horizontal here
		TEdge* ePrev = horzEdge->PrevInAEL;
		TEdge* eNext = horzEdge->NextInAEL;
		if (ePrev && ePrev->Curr.X == horzEdge->Bot.X &&
			ePrev->Curr.Y == horzEdge->Bot.Y && ePrev->WindDelta != 0 &&
			(ePrev->OutIdx >= 0 && ePrev->Curr.Y > ePrev->Top.Y &&
			 SlopesEqual(*horzEdge, *ePrev, m_UseFullRange)))
		{
		    OutPt* op2 = AddOutPt(ePrev, horzEdge->Bot);
		    AddJoin(op1, op2, horzEdge->Top);
		}
		else if (eNext && eNext->Curr.X == horzEdge->Bot.X &&
			eNext->Curr.Y == horzEdge->Bot.Y && eNext->WindDelta != 0 &&
			eNext->OutIdx >= 0 && eNext->Curr.Y > eNext->Top.Y &&
			SlopesEqual(*horzEdge, *eNext, m_UseFullRange))
		{
		    OutPt* op2 = AddOutPt(eNext, horzEdge->Bot);
		    AddJoin(op1, op2, horzEdge->Top);
		}
	    }
	    else
		UpdateEdgeIntoAEL(horzEdge);
	}
	else
	{
	    if (horzEdge->OutIdx >= 0) AddOutPt(horzEdge, horzEdge->Top);
	    DeleteFromAEL(horzEdge);
	}
    }
    //------------------------------------------------------------------------------

    bool Clipper::ProcessIntersections(const cInt topY)
    {
	if( !m_ActiveEdges ) return true;
	try {
	    BuildIntersectList(topY);
	    size_t IlSize = m_IntersectList.size();
	    if (IlSize == 0) return true;
	    if (IlSize == 1 || FixupIntersectionOrder()) ProcessIntersectList();
	    else return false;
	}
	catch(...)
	{
	    m_SortedEdges = 0;
	    DisposeIntersectNodes();
	    throw clipperException("ProcessIntersections error");
	}
	m_SortedEdges = 0;
	return true;
    }
    //------------------------------------------------------------------------------

    void Clipper::DisposeIntersectNodes()
    {
	for (size_t i = 0; i < m_IntersectList.size(); ++i )
	    delete m_IntersectList[i];
	m_IntersectList.clear();
    }
    //------------------------------------------------------------------------------

    void Clipper::BuildIntersectList(const cInt topY)
    {
	if ( !m_ActiveEdges ) return;

	//prepare for sorting ...
	TEdge* e = m_ActiveEdges;
	m_SortedEdges = e;
	while( e )
	{
	    e->PrevInSEL = e->PrevInAEL;
	    e->NextInSEL = e->NextInAEL;
	    e->Curr.X = TopX( *e, topY );
	    e = e->NextInAEL;
	}

	//bubblesort ...
	bool isModified;
	do
	{
	    isModified = false;
	    e = m_SortedEdges;
	    while( e->NextInSEL )
	    {
		TEdge *eNext = e->NextInSEL;
		IntPoint Pt;
		if(e->Curr.X > eNext->Curr.X)
		{
		    IntersectPoint(*e, *eNext, Pt);
		    if (Pt.Y < topY) Pt = IntPoint(TopX(*e, topY), topY);
		    IntersectNode * newNode = new IntersectNode;
		    newNode->Edge1 = e;
		    newNode->Edge2 = eNext;
		    newNode->Pt = Pt;
		    m_IntersectList.push_back(newNode);

		    SwapPositionsInSEL(e, eNext);
		    isModified = true;
		}
		else
		    e = eNext;
	    }
	    if( e->PrevInSEL ) e->PrevInSEL->NextInSEL = 0;
	    else break;
	}
	while ( isModified );
	m_SortedEdges = 0; //important
    }
    //------------------------------------------------------------------------------


    void Clipper::ProcessIntersectList()
    {
	for (size_t i = 0; i < m_IntersectList.size(); ++i)
	{
	    IntersectNode* iNode = m_IntersectList[i];
	    {
		IntersectEdges( iNode->Edge1, iNode->Edge2, iNode->Pt);
		SwapPositionsInAEL( iNode->Edge1 , iNode->Edge2 );
	    }
	    delete iNode;
	}
	m_IntersectList.clear();
    }
    //------------------------------------------------------------------------------

    bool IntersectListSort(IntersectNode* node1, IntersectNode* node2)
    {
	return node2->Pt.Y < node1->Pt.Y;
    }
    //------------------------------------------------------------------------------

    inline bool EdgesAdjacent(const IntersectNode &inode)
    {
	return (inode.Edge1->NextInSEL == inode.Edge2) ||
	    (inode.Edge1->PrevInSEL == inode.Edge2);
    }
    //------------------------------------------------------------------------------

    bool Clipper::FixupIntersectionOrder()
    {
	//pre-condition: intersections are sorted Bottom-most first.
	//Now it's crucial that intersections are made only between adjacent edges,
	//so to ensure this the order of intersections may need adjusting ...
	CopyAELToSEL();
	std::sort(m_IntersectList.begin(), m_IntersectList.end(), IntersectListSort);
	size_t cnt = m_IntersectList.size();
	for (size_t i = 0; i < cnt; ++i)
	{
	    if (!EdgesAdjacent(*m_IntersectList[i]))
	    {
		size_t j = i + 1;
		while (j < cnt && !EdgesAdjacent(*m_IntersectList[j])) j++;
		if (j == cnt)  return false;
		std::swap(m_IntersectList[i], m_IntersectList[j]);
	    }
	    SwapPositionsInSEL(m_IntersectList[i]->Edge1, m_IntersectList[i]->Edge2);
	}
	return true;
    }
    //------------------------------------------------------------------------------

    void Clipper::DoMaxima(TEdge *e)
    {
	TEdge* eMaxPair = GetMaximaPairEx(e);
	if (!eMaxPair)
	{
	    if (e->OutIdx >= 0)
		AddOutPt(e, e->Top);
	    DeleteFromAEL(e);
	    return;
	}

	TEdge* eNext = e->NextInAEL;
	while(eNext && eNext != eMaxPair)
	{
	    IntersectEdges(e, eNext, e->Top);
	    SwapPositionsInAEL(e, eNext);
	    eNext = e->NextInAEL;
	}

	if(e->OutIdx == Unassigned && eMaxPair->OutIdx == Unassigned)
	{
	    DeleteFromAEL(e);
	    DeleteFromAEL(eMaxPair);
	}
	else if( e->OutIdx >= 0 && eMaxPair->OutIdx >= 0 )
	{
	    if (e->OutIdx >= 0) AddLocalMaxPoly(e, eMaxPair, e->Top);
	    DeleteFromAEL(e);
	    DeleteFromAEL(eMaxPair);
	}
#ifdef use_lines
	else if (e->WindDelta == 0)
	{
	    if (e->OutIdx >= 0)
	    {
		AddOutPt(e, e->Top);
		e->OutIdx = Unassigned;
	    }
	    DeleteFromAEL(e);

	    if (eMaxPair->OutIdx >= 0)
	    {
		AddOutPt(eMaxPair, e->Top);
		eMaxPair->OutIdx = Unassigned;
	    }
	    DeleteFromAEL(eMaxPair);
	}
#endif
	else throw clipperException("DoMaxima error");
    }
    //------------------------------------------------------------------------------

    void Clipper::ProcessEdgesAtTopOfScanbeam(const cInt topY)
    {
	TEdge* e = m_ActiveEdges;
	while( e )
	{
	    //1. process maxima, treating them as if they're 'bent' horizontal edges,
	    //   but exclude maxima with horizontal edges. nb: e can't be a horizontal.
	    bool IsMaximaEdge = IsMaxima(e, topY);

	    if(IsMaximaEdge)
	    {
		TEdge* eMaxPair = GetMaximaPairEx(e);
		IsMaximaEdge = (!eMaxPair || !IsHorizontal(*eMaxPair));
	    }

	    if(IsMaximaEdge)
	    {
		if (m_StrictSimple) m_Maxima.push_back(e->Top.X);
		TEdge* ePrev = e->PrevInAEL;
		DoMaxima(e);
		if( !ePrev ) e = m_ActiveEdges;
		else e = ePrev->NextInAEL;
	    }
	    else
	    {
		//2. promote horizontal edges, otherwise update Curr.X and Curr.Y ...
		if (IsIntermediate(e, topY) && IsHorizontal(*e->NextInLML))
		{
		    UpdateEdgeIntoAEL(e);
		    if (e->OutIdx >= 0)
			AddOutPt(e, e->Bot);
		    AddEdgeToSEL(e);
		}
		else
		{
		    e->Curr.X = TopX( *e, topY );
		    e->Curr.Y = topY;
#ifdef use_xyz
		    e->Curr.Z = topY == e->Top.Y ? e->Top.Z : (topY == e->Bot.Y ? e->Bot.Z : 0);
#endif
		}

		//When StrictlySimple and 'e' is being touched by another edge, then
		//make sure both edges have a vertex here ...
		if (m_StrictSimple)
		{
		    TEdge* ePrev = e->PrevInAEL;
		    if ((e->OutIdx >= 0) && (e->WindDelta != 0) && ePrev && (ePrev->OutIdx >= 0) &&
			    (ePrev->Curr.X == e->Curr.X) && (ePrev->WindDelta != 0))
		    {
			IntPoint pt = e->Curr;
#ifdef use_xyz
			SetZ(pt, *ePrev, *e);
#endif
			OutPt* op = AddOutPt(ePrev, pt);
			OutPt* op2 = AddOutPt(e, pt);
			AddJoin(op, op2, pt); //StrictlySimple (type-3) join
		    }
		}

		e = e->NextInAEL;
	    }
	}

	//3. Process horizontals at the Top of the scanbeam ...
	m_Maxima.sort();
	ProcessHorizontals();
	m_Maxima.clear();

	//4. Promote intermediate vertices ...
	e = m_ActiveEdges;
	while(e)
	{
	    if(IsIntermediate(e, topY))
	    {
		OutPt* op = 0;
		if( e->OutIdx >= 0 )
		    op = AddOutPt(e, e->Top);
		UpdateEdgeIntoAEL(e);

		//if output polygons share an edge, they'll need joining later ...
		TEdge* ePrev = e->PrevInAEL;
		TEdge* eNext = e->NextInAEL;
		if (ePrev && ePrev->Curr.X == e->Bot.X &&
			ePrev->Curr.Y == e->Bot.Y && op &&
			ePrev->OutIdx >= 0 && ePrev->Curr.Y > ePrev->Top.Y &&
			SlopesEqual(e->Curr, e->Top, ePrev->Curr, ePrev->Top, m_UseFullRange) &&
			(e->WindDelta != 0) && (ePrev->WindDelta != 0))
		{
		    OutPt* op2 = AddOutPt(ePrev, e->Bot);
		    AddJoin(op, op2, e->Top);
		}
		else if (eNext && eNext->Curr.X == e->Bot.X &&
			eNext->Curr.Y == e->Bot.Y && op &&
			eNext->OutIdx >= 0 && eNext->Curr.Y > eNext->Top.Y &&
			SlopesEqual(e->Curr, e->Top, eNext->Curr, eNext->Top, m_UseFullRange) &&
			(e->WindDelta != 0) && (eNext->WindDelta != 0))
		{
		    OutPt* op2 = AddOutPt(eNext, e->Bot);
		    AddJoin(op, op2, e->Top);
		}
	    }
	    e = e->NextInAEL;
	}
    }
    //------------------------------------------------------------------------------

    void Clipper::FixupOutPolyline(OutRec &outrec)
    {
	OutPt *pp = outrec.Pts;
	OutPt *lastPP = pp->Prev;
	while (pp != lastPP)
	{
	    pp = pp->Next;
	    if (pp->Pt == pp->Prev->Pt)
	    {
		if (pp == lastPP) lastPP = pp->Prev;
		OutPt *tmpPP = pp->Prev;
		tmpPP->Next = pp->Next;
		pp->Next->Prev = tmpPP;
		delete pp;
		pp = tmpPP;
	    }
	}

	if (pp == pp->Prev)
	{
	    DisposeOutPts(pp);
	    outrec.Pts = 0;
	    return;
	}
    }
    //------------------------------------------------------------------------------

    void Clipper::FixupOutPolygon(OutRec &outrec)
    {
	//FixupOutPolygon() - removes duplicate points and simplifies consecutive
	//parallel edges by removing the middle vertex.
	OutPt *lastOK = 0;
	outrec.BottomPt = 0;
	OutPt *pp = outrec.Pts;
	bool preserveCol = m_PreserveCollinear || m_StrictSimple;

	for (;;)
	{
	    if (pp->Prev == pp || pp->Prev == pp->Next)
	    {
		DisposeOutPts(pp);
		outrec.Pts = 0;
		return;
	    }

	    //test for duplicate points and collinear edges ...
	    if ((pp->Pt == pp->Next->Pt) || (pp->Pt == pp->Prev->Pt) ||
		    (SlopesEqual(pp->Prev->Pt, pp->Pt, pp->Next->Pt, m_UseFullRange) &&
		     (!preserveCol || !Pt2IsBetweenPt1AndPt3(pp->Prev->Pt, pp->Pt, pp->Next->Pt))))
	    {
		lastOK = 0;
		OutPt *tmp = pp;
		pp->Prev->Next = pp->Next;
		pp->Next->Prev = pp->Prev;
		pp = pp->Prev;
		delete tmp;
	    }
	    else if (pp == lastOK) break;
	    else
	    {
		if (!lastOK) lastOK = pp;
		pp = pp->Next;
	    }
	}
	outrec.Pts = pp;
    }
    //------------------------------------------------------------------------------

    int PointCount(OutPt *Pts)
    {
	if (!Pts) return 0;
	int result = 0;
	OutPt* p = Pts;
	do
	{
	    result++;
	    p = p->Next;
	}
	while (p != Pts);
	return result;
    }
    //------------------------------------------------------------------------------

    void Clipper::BuildResult(Paths &polys)
    {
	polys.reserve(m_PolyOuts.size());
	for (PolyOutList::size_type i = 0; i < m_PolyOuts.size(); ++i)
	{
	    if (!m_PolyOuts[i]->Pts) continue;
	    Path pg;
	    OutPt* p = m_PolyOuts[i]->Pts->Prev;
	    int cnt = PointCount(p);
	    if (cnt < 2) continue;
	    pg.reserve(cnt);
	    for (int ii = 0; ii < cnt; ++ii)
	    {
		pg.push_back(p->Pt);
		p = p->Prev;
	    }
	    polys.push_back(pg);
	}
    }
    //------------------------------------------------------------------------------

    void Clipper::BuildResult2(PolyTree& polytree)
    {
	polytree.Clear();
	polytree.AllNodes.reserve(m_PolyOuts.size());
	//add each output polygon/contour to polytree ...
	for (PolyOutList::size_type i = 0; i < m_PolyOuts.size(); i++)
	{
	    OutRec* outRec = m_PolyOuts[i];
	    int cnt = PointCount(outRec->Pts);
	    if ((outRec->IsOpen && cnt < 2) || (!outRec->IsOpen && cnt < 3)) continue;
	    FixHoleLinkage(*outRec);
	    PolyNode* pn = new PolyNode();
	    //nb: polytree takes ownership of all the PolyNodes
	    polytree.AllNodes.push_back(pn);
	    outRec->PolyNd = pn;
	    pn->Parent = 0;
	    pn->Index = 0;
	    pn->Contour.reserve(cnt);
	    OutPt *op = outRec->Pts->Prev;
	    for (int j = 0; j < cnt; j++)
	    {
		pn->Contour.push_back(op->Pt);
		op = op->Prev;
	    }
	}

	//fixup PolyNode links etc ...
	polytree.Childs.reserve(m_PolyOuts.size());
	for (PolyOutList::size_type i = 0; i < m_PolyOuts.size(); i++)
	{
	    OutRec* outRec = m_PolyOuts[i];
	    if (!outRec->PolyNd) continue;
	    if (outRec->IsOpen)
	    {
		outRec->PolyNd->m_IsOpen = true;
		polytree.AddChild(*outRec->PolyNd);
	    }
	    else if (outRec->FirstLeft && outRec->FirstLeft->PolyNd)
		outRec->FirstLeft->PolyNd->AddChild(*outRec->PolyNd);
	    else
		polytree.AddChild(*outRec->PolyNd);
	}
    }
    //------------------------------------------------------------------------------

    void SwapIntersectNodes(IntersectNode &int1, IntersectNode &int2)
    {
	//just swap the contents (because fIntersectNodes is a single-linked-list)
	IntersectNode inode = int1; //gets a copy of Int1
	int1.Edge1 = int2.Edge1;
	int1.Edge2 = int2.Edge2;
	int1.Pt = int2.Pt;
	int2.Edge1 = inode.Edge1;
	int2.Edge2 = inode.Edge2;
	int2.Pt = inode.Pt;
    }
    //------------------------------------------------------------------------------

    inline bool E2InsertsBeforeE1(TEdge &e1, TEdge &e2)
    {
	if (e2.Curr.X == e1.Curr.X)
	{
	    if (e2.Top.Y > e1.Top.Y)
		return e2.Top.X < TopX(e1, e2.Top.Y);
	    else return e1.Top.X > TopX(e2, e1.Top.Y);
	}
	else return e2.Curr.X < e1.Curr.X;
    }
    //------------------------------------------------------------------------------

    bool GetOverlap(const cInt a1, const cInt a2, const cInt b1, const cInt b2,
	    cInt& Left, cInt& Right)
    {
	if (a1 < a2)
	{
	    if (b1 < b2) {Left = std::max(a1,b1); Right = std::min(a2,b2);}
	    else {Left = std::max(a1,b2); Right = std::min(a2,b1);}
	}
	else
	{
	    if (b1 < b2) {Left = std::max(a2,b1); Right = std::min(a1,b2);}
	    else {Left = std::max(a2,b2); Right = std::min(a1,b1);}
	}
	return Left < Right;
    }
    //------------------------------------------------------------------------------

    inline void UpdateOutPtIdxs(OutRec& outrec)
    {
	OutPt* op = outrec.Pts;
	do
	{
	    op->Idx = outrec.Idx;
	    op = op->Prev;
	}
	while(op != outrec.Pts);
    }
    //------------------------------------------------------------------------------

    void Clipper::InsertEdgeIntoAEL(TEdge *edge, TEdge* startEdge)
    {
	if(!m_ActiveEdges)
	{
	    edge->PrevInAEL = 0;
	    edge->NextInAEL = 0;
	    m_ActiveEdges = edge;
	}
	else if(!startEdge && E2InsertsBeforeE1(*m_ActiveEdges, *edge))
	{
	    edge->PrevInAEL = 0;
	    edge->NextInAEL = m_ActiveEdges;
	    m_ActiveEdges->PrevInAEL = edge;
	    m_ActiveEdges = edge;
	}
	else
	{
	    if(!startEdge) startEdge = m_ActiveEdges;
	    while(startEdge->NextInAEL  &&
		    !E2InsertsBeforeE1(*startEdge->NextInAEL , *edge))
		startEdge = startEdge->NextInAEL;
	    edge->NextInAEL = startEdge->NextInAEL;
	    if(startEdge->NextInAEL) startEdge->NextInAEL->PrevInAEL = edge;
	    edge->PrevInAEL = startEdge;
	    startEdge->NextInAEL = edge;
	}
    }
    //----------------------------------------------------------------------

    OutPt* DupOutPt(OutPt* outPt, bool InsertAfter)
    {
	OutPt* result = new OutPt;
	result->Pt = outPt->Pt;
	result->Idx = outPt->Idx;
	if (InsertAfter)
	{
	    result->Next = outPt->Next;
	    result->Prev = outPt;
	    outPt->Next->Prev = result;
	    outPt->Next = result;
	}
	else
	{
	    result->Prev = outPt->Prev;
	    result->Next = outPt;
	    outPt->Prev->Next = result;
	    outPt->Prev = result;
	}
	return result;
    }
    //------------------------------------------------------------------------------

    bool JoinHorz(OutPt* op1, OutPt* op1b, OutPt* op2, OutPt* op2b,
	    const IntPoint Pt, bool DiscardLeft)
    {
	Direction Dir1 = (op1->Pt.X > op1b->Pt.X ? dRightToLeft : dLeftToRight);
	Direction Dir2 = (op2->Pt.X > op2b->Pt.X ? dRightToLeft : dLeftToRight);
	if (Dir1 == Dir2) return false;

	//When DiscardLeft, we want Op1b to be on the Left of Op1, otherwise we
	//want Op1b to be on the Right. (And likewise with Op2 and Op2b.)
	//So, to facilitate this while inserting Op1b and Op2b ...
	//when DiscardLeft, make sure we're AT or RIGHT of Pt before adding Op1b,
	//otherwise make sure we're AT or LEFT of Pt. (Likewise with Op2b.)
	if (Dir1 == dLeftToRight)
	{
	    while (op1->Next->Pt.X <= Pt.X &&
		    op1->Next->Pt.X >= op1->Pt.X && op1->Next->Pt.Y == Pt.Y)
		op1 = op1->Next;
	    if (DiscardLeft && (op1->Pt.X != Pt.X)) op1 = op1->Next;
	    op1b = DupOutPt(op1, !DiscardLeft);
	    if (op1b->Pt != Pt)
	    {
		op1 = op1b;
		op1->Pt = Pt;
		op1b = DupOutPt(op1, !DiscardLeft);
	    }
	}
	else
	{
	    while (op1->Next->Pt.X >= Pt.X &&
		    op1->Next->Pt.X <= op1->Pt.X && op1->Next->Pt.Y == Pt.Y)
		op1 = op1->Next;
	    if (!DiscardLeft && (op1->Pt.X != Pt.X)) op1 = op1->Next;
	    op1b = DupOutPt(op1, DiscardLeft);
	    if (op1b->Pt != Pt)
	    {
		op1 = op1b;
		op1->Pt = Pt;
		op1b = DupOutPt(op1, DiscardLeft);
	    }
	}

	if (Dir2 == dLeftToRight)
	{
	    while (op2->Next->Pt.X <= Pt.X &&
		    op2->Next->Pt.X >= op2->Pt.X && op2->Next->Pt.Y == Pt.Y)
		op2 = op2->Next;
	    if (DiscardLeft && (op2->Pt.X != Pt.X)) op2 = op2->Next;
	    op2b = DupOutPt(op2, !DiscardLeft);
	    if (op2b->Pt != Pt)
	    {
		op2 = op2b;
		op2->Pt = Pt;
		op2b = DupOutPt(op2, !DiscardLeft);
	    };
	} else
	{
	    while (op2->Next->Pt.X >= Pt.X &&
		    op2->Next->Pt.X <= op2->Pt.X && op2->Next->Pt.Y == Pt.Y)
		op2 = op2->Next;
	    if (!DiscardLeft && (op2->Pt.X != Pt.X)) op2 = op2->Next;
	    op2b = DupOutPt(op2, DiscardLeft);
	    if (op2b->Pt != Pt)
	    {
		op2 = op2b;
		op2->Pt = Pt;
		op2b = DupOutPt(op2, DiscardLeft);
	    };
	};

	if ((Dir1 == dLeftToRight) == DiscardLeft)
	{
	    op1->Prev = op2;
	    op2->Next = op1;
	    op1b->Next = op2b;
	    op2b->Prev = op1b;
	}
	else
	{
	    op1->Next = op2;
	    op2->Prev = op1;
	    op1b->Prev = op2b;
	    op2b->Next = op1b;
	}
	return true;
    }
    //------------------------------------------------------------------------------

    bool Clipper::JoinPoints(Join *j, OutRec* outRec1, OutRec* outRec2)
    {
	OutPt *op1 = j->OutPt1, *op1b;
	OutPt *op2 = j->OutPt2, *op2b;

	//There are 3 kinds of joins for output polygons ...
	//1. Horizontal joins where Join.OutPt1 & Join.OutPt2 are vertices anywhere
	//along (horizontal) collinear edges (& Join.OffPt is on the same horizontal).
	//2. Non-horizontal joins where Join.OutPt1 & Join.OutPt2 are at the same
	//location at the Bottom of the overlapping segment (& Join.OffPt is above).
	//3. StrictSimple joins where edges touch but are not collinear and where
	//Join.OutPt1, Join.OutPt2 & Join.OffPt all share the same point.
	bool isHorizontal = (j->OutPt1->Pt.Y == j->OffPt.Y);

	if (isHorizontal  && (j->OffPt == j->OutPt1->Pt) &&
		(j->OffPt == j->OutPt2->Pt))
	{
	    //Strictly Simple join ...
	    if (outRec1 != outRec2) return false;
	    op1b = j->OutPt1->Next;
	    while (op1b != op1 && (op1b->Pt == j->OffPt))
		op1b = op1b->Next;
	    bool reverse1 = (op1b->Pt.Y > j->OffPt.Y);
	    op2b = j->OutPt2->Next;
	    while (op2b != op2 && (op2b->Pt == j->OffPt))
		op2b = op2b->Next;
	    bool reverse2 = (op2b->Pt.Y > j->OffPt.Y);
	    if (reverse1 == reverse2) return false;
	    if (reverse1)
	    {
		op1b = DupOutPt(op1, false);
		op2b = DupOutPt(op2, true);
		op1->Prev = op2;
		op2->Next = op1;
		op1b->Next = op2b;
		op2b->Prev = op1b;
		j->OutPt1 = op1;
		j->OutPt2 = op1b;
		return true;
	    } else
	    {
		op1b = DupOutPt(op1, true);
		op2b = DupOutPt(op2, false);
		op1->Next = op2;
		op2->Prev = op1;
		op1b->Prev = op2b;
		op2b->Next = op1b;
		j->OutPt1 = op1;
		j->OutPt2 = op1b;
		return true;
	    }
	}
	else if (isHorizontal)
	{
	    //treat horizontal joins differently to non-horizontal joins since with
	    //them we're not yet sure where the overlapping is. OutPt1.Pt & OutPt2.Pt
	    //may be anywhere along the horizontal edge.
	    op1b = op1;
	    while (op1->Prev->Pt.Y == op1->Pt.Y && op1->Prev != op1b && op1->Prev != op2)
		op1 = op1->Prev;
	    while (op1b->Next->Pt.Y == op1b->Pt.Y && op1b->Next != op1 && op1b->Next != op2)
		op1b = op1b->Next;
	    if (op1b->Next == op1 || op1b->Next == op2) return false; //a flat 'polygon'

	    op2b = op2;
	    while (op2->Prev->Pt.Y == op2->Pt.Y && op2->Prev != op2b && op2->Prev != op1b)
		op2 = op2->Prev;
	    while (op2b->Next->Pt.Y == op2b->Pt.Y && op2b->Next != op2 && op2b->Next != op1)
		op2b = op2b->Next;
	    if (op2b->Next == op2 || op2b->Next == op1) return false; //a flat 'polygon'

	    cInt Left, Right;
	    //Op1 --> Op1b & Op2 --> Op2b are the extremites of the horizontal edges
	    if (!GetOverlap(op1->Pt.X, op1b->Pt.X, op2->Pt.X, op2b->Pt.X, Left, Right))
		return false;

	    //DiscardLeftSide: when overlapping edges are joined, a spike will created
	    //which needs to be cleaned up. However, we don't want Op1 or Op2 caught up
	    //on the discard Side as either may still be needed for other joins ...
	    IntPoint Pt;
	    bool DiscardLeftSide;
	    if (op1->Pt.X >= Left && op1->Pt.X <= Right)
	    {
		Pt = op1->Pt; DiscardLeftSide = (op1->Pt.X > op1b->Pt.X);
	    }
	    else if (op2->Pt.X >= Left&& op2->Pt.X <= Right)
	    {
		Pt = op2->Pt; DiscardLeftSide = (op2->Pt.X > op2b->Pt.X);
	    }
	    else if (op1b->Pt.X >= Left && op1b->Pt.X <= Right)
	    {
		Pt = op1b->Pt; DiscardLeftSide = op1b->Pt.X > op1->Pt.X;
	    }
	    else
	    {
		Pt = op2b->Pt; DiscardLeftSide = (op2b->Pt.X > op2->Pt.X);
	    }
	    j->OutPt1 = op1; j->OutPt2 = op2;
	    return JoinHorz(op1, op1b, op2, op2b, Pt, DiscardLeftSide);
	} else
	{
	    //nb: For non-horizontal joins ...
	    //    1. Jr.OutPt1.Pt.Y == Jr.OutPt2.Pt.Y
	    //    2. Jr.OutPt1.Pt > Jr.OffPt.Y

	    //make sure the polygons are correctly oriented ...
	    op1b = op1->Next;
	    while ((op1b->Pt == op1->Pt) && (op1b != op1)) op1b = op1b->Next;
	    bool Reverse1 = ((op1b->Pt.Y > op1->Pt.Y) ||
		    !SlopesEqual(op1->Pt, op1b->Pt, j->OffPt, m_UseFullRange));
	    if (Reverse1)
	    {
		op1b = op1->Prev;
		while ((op1b->Pt == op1->Pt) && (op1b != op1)) op1b = op1b->Prev;
		if ((op1b->Pt.Y > op1->Pt.Y) ||
			!SlopesEqual(op1->Pt, op1b->Pt, j->OffPt, m_UseFullRange)) return false;
	    };
	    op2b = op2->Next;
	    while ((op2b->Pt == op2->Pt) && (op2b != op2))op2b = op2b->Next;
	    bool Reverse2 = ((op2b->Pt.Y > op2->Pt.Y) ||
		    !SlopesEqual(op2->Pt, op2b->Pt, j->OffPt, m_UseFullRange));
	    if (Reverse2)
	    {
		op2b = op2->Prev;
		while ((op2b->Pt == op2->Pt) && (op2b != op2)) op2b = op2b->Prev;
		if ((op2b->Pt.Y > op2->Pt.Y) ||
			!SlopesEqual(op2->Pt, op2b->Pt, j->OffPt, m_UseFullRange)) return false;
	    }

	    if ((op1b == op1) || (op2b == op2) || (op1b == op2b) ||
		    ((outRec1 == outRec2) && (Reverse1 == Reverse2))) return false;

	    if (Reverse1)
	    {
		op1b = DupOutPt(op1, false);
		op2b = DupOutPt(op2, true);
		op1->Prev = op2;
		op2->Next = op1;
		op1b->Next = op2b;
		op2b->Prev = op1b;
		j->OutPt1 = op1;
		j->OutPt2 = op1b;
		return true;
	    } else
	    {
		op1b = DupOutPt(op1, true);
		op2b = DupOutPt(op2, false);
		op1->Next = op2;
		op2->Prev = op1;
		op1b->Prev = op2b;
		op2b->Next = op1b;
		j->OutPt1 = op1;
		j->OutPt2 = op1b;
		return true;
	    }
	}
    }
    //----------------------------------------------------------------------

    static OutRec* ParseFirstLeft(OutRec* FirstLeft)
    {
	while (FirstLeft && !FirstLeft->Pts)
	    FirstLeft = FirstLeft->FirstLeft;
	return FirstLeft;
    }
    //------------------------------------------------------------------------------

    void Clipper::FixupFirstLefts1(OutRec* OldOutRec, OutRec* NewOutRec)
    {
	//tests if NewOutRec contains the polygon before reassigning FirstLeft
	for (PolyOutList::size_type i = 0; i < m_PolyOuts.size(); ++i)
	{
	    OutRec* outRec = m_PolyOuts[i];
	    OutRec* firstLeft = ParseFirstLeft(outRec->FirstLeft);
	    if (outRec->Pts  && firstLeft == OldOutRec)
	    {
		if (Poly2ContainsPoly1(outRec->Pts, NewOutRec->Pts))
		    outRec->FirstLeft = NewOutRec;
	    }
	}
    }
    //----------------------------------------------------------------------

    void Clipper::FixupFirstLefts2(OutRec* InnerOutRec, OutRec* OuterOutRec)
    {
	//A polygon has split into two such that one is now the inner of the other.
	//It's possible that these polygons now wrap around other polygons, so check
	//every polygon that's also contained by OuterOutRec's FirstLeft container
	//(including 0) to see if they've become inner to the new inner polygon ...
	OutRec* orfl = OuterOutRec->FirstLeft;
	for (PolyOutList::size_type i = 0; i < m_PolyOuts.size(); ++i)
	{
	    OutRec* outRec = m_PolyOuts[i];

	    if (!outRec->Pts || outRec == OuterOutRec || outRec == InnerOutRec)
		continue;
	    OutRec* firstLeft = ParseFirstLeft(outRec->FirstLeft);
	    if (firstLeft != orfl && firstLeft != InnerOutRec && firstLeft != OuterOutRec)
		continue;
	    if (Poly2ContainsPoly1(outRec->Pts, InnerOutRec->Pts))
		outRec->FirstLeft = InnerOutRec;
	    else if (Poly2ContainsPoly1(outRec->Pts, OuterOutRec->Pts))
		outRec->FirstLeft = OuterOutRec;
	    else if (outRec->FirstLeft == InnerOutRec || outRec->FirstLeft == OuterOutRec)
		outRec->FirstLeft = orfl;
	}
    }
    //----------------------------------------------------------------------
    void Clipper::FixupFirstLefts3(OutRec* OldOutRec, OutRec* NewOutRec)
    {
	//reassigns FirstLeft WITHOUT testing if NewOutRec contains the polygon
	for (PolyOutList::size_type i = 0; i < m_PolyOuts.size(); ++i)
	{
	    OutRec* outRec = m_PolyOuts[i];
	    OutRec* firstLeft = ParseFirstLeft(outRec->FirstLeft);
	    if (outRec->Pts && firstLeft == OldOutRec)
		outRec->FirstLeft = NewOutRec;
	}
    }
    //----------------------------------------------------------------------

    void Clipper::JoinCommonEdges()
    {
	for (JoinList::size_type i = 0; i < m_Joins.size(); i++)
	{
	    Join* join = m_Joins[i];

	    OutRec *outRec1 = GetOutRec(join->OutPt1->Idx);
	    OutRec *outRec2 = GetOutRec(join->OutPt2->Idx);

	    if (!outRec1->Pts || !outRec2->Pts) continue;
	    if (outRec1->IsOpen || outRec2->IsOpen) continue;

	    //get the polygon fragment with the correct hole state (FirstLeft)
	    //before calling JoinPoints() ...
	    OutRec *holeStateRec;
	    if (outRec1 == outRec2) holeStateRec = outRec1;
	    else if (OutRec1RightOfOutRec2(outRec1, outRec2)) holeStateRec = outRec2;
	    else if (OutRec1RightOfOutRec2(outRec2, outRec1)) holeStateRec = outRec1;
	    else holeStateRec = GetLowermostRec(outRec1, outRec2);

	    if (!JoinPoints(join, outRec1, outRec2)) continue;

	    if (outRec1 == outRec2)
	    {
		//instead of joining two polygons, we've just created a new one by
		//splitting one polygon into two.
		outRec1->Pts = join->OutPt1;
		outRec1->BottomPt = 0;
		outRec2 = CreateOutRec();
		outRec2->Pts = join->OutPt2;

		//update all OutRec2.Pts Idx's ...
		UpdateOutPtIdxs(*outRec2);

		if (Poly2ContainsPoly1(outRec2->Pts, outRec1->Pts))
		{
		    //outRec1 contains outRec2 ...
		    outRec2->IsHole = !outRec1->IsHole;
		    outRec2->FirstLeft = outRec1;

		    if (m_UsingPolyTree) FixupFirstLefts2(outRec2, outRec1);

		    if ((outRec2->IsHole ^ m_ReverseOutput) == (Area(*outRec2) > 0))
			ReversePolyPtLinks(outRec2->Pts);

		} else if (Poly2ContainsPoly1(outRec1->Pts, outRec2->Pts))
		{
		    //outRec2 contains outRec1 ...
		    outRec2->IsHole = outRec1->IsHole;
		    outRec1->IsHole = !outRec2->IsHole;
		    outRec2->FirstLeft = outRec1->FirstLeft;
		    outRec1->FirstLeft = outRec2;

		    if (m_UsingPolyTree) FixupFirstLefts2(outRec1, outRec2);

		    if ((outRec1->IsHole ^ m_ReverseOutput) == (Area(*outRec1) > 0))
			ReversePolyPtLinks(outRec1->Pts);
		}
		else
		{
		    //the 2 polygons are completely separate ...
		    outRec2->IsHole = outRec1->IsHole;
		    outRec2->FirstLeft = outRec1->FirstLeft;

		    //fixup FirstLeft pointers that may need reassigning to OutRec2
		    if (m_UsingPolyTree) FixupFirstLefts1(outRec1, outRec2);
		}

	    } else
	    {
		//joined 2 polygons together ...

		outRec2->Pts = 0;
		outRec2->BottomPt = 0;
		outRec2->Idx = outRec1->Idx;

		outRec1->IsHole = holeStateRec->IsHole;
		if (holeStateRec == outRec2)
		    outRec1->FirstLeft = outRec2->FirstLeft;
		outRec2->FirstLeft = outRec1;

		if (m_UsingPolyTree) FixupFirstLefts3(outRec2, outRec1);
	    }
	}
    }

    //------------------------------------------------------------------------------
    // ClipperOffset support functions ...
    //------------------------------------------------------------------------------

    DoublePoint GetUnitNormal(const IntPoint &pt1, const IntPoint &pt2)
    {
	if(pt2.X == pt1.X && pt2.Y == pt1.Y)
	    return DoublePoint(0, 0);

	double Dx = (double)(pt2.X - pt1.X);
	double dy = (double)(pt2.Y - pt1.Y);
	double f = 1 *1.0/ std::sqrt( Dx*Dx + dy*dy );
	Dx *= f;
	dy *= f;
	return DoublePoint(dy, -Dx);
    }

    //------------------------------------------------------------------------------
    // ClipperOffset class
    //------------------------------------------------------------------------------

    ClipperOffset::ClipperOffset(double miterLimit, double arcTolerance)
    {
	this->MiterLimit = miterLimit;
	this->ArcTolerance = arcTolerance;
	m_lowest.X = -1;
    }
    //------------------------------------------------------------------------------

    ClipperOffset::~ClipperOffset()
    {
	Clear();
    }
    //------------------------------------------------------------------------------

    void ClipperOffset::Clear()
    {
	for (int i = 0; i < m_polyNodes.ChildCount(); ++i)
	    delete m_polyNodes.Childs[i];
	m_polyNodes.Childs.clear();
	m_lowest.X = -1;
    }
    //------------------------------------------------------------------------------

    void ClipperOffset::AddPath(const Path& path, JoinType joinType, EndType endType)
    {
	int highI = (int)path.size() - 1;
	if (highI < 0) return;
	PolyNode* newNode = new PolyNode();
	newNode->m_jointype = joinType;
	newNode->m_endtype = endType;

	//strip duplicate points from path and also get index to the lowest point ...
	if (endType == etClosedLine || endType == etClosedPolygon)
	    while (highI > 0 && path[0] == path[highI]) highI--;
	newNode->Contour.reserve(highI + 1);
	newNode->Contour.push_back(path[0]);
	int j = 0, k = 0;
	for (int i = 1; i <= highI; i++)
	    if (newNode->Contour[j] != path[i])
	    {
		j++;
		newNode->Contour.push_back(path[i]);
		if (path[i].Y > newNode->Contour[k].Y ||
			(path[i].Y == newNode->Contour[k].Y &&
			 path[i].X < newNode->Contour[k].X)) k = j;
	    }
	if (endType == etClosedPolygon && j < 2)
	{
	    delete newNode;
	    return;
	}
	m_polyNodes.AddChild(*newNode);

	//if this path's lowest pt is lower than all the others then update m_lowest
	if (endType != etClosedPolygon) return;
	if (m_lowest.X < 0)
	    m_lowest = IntPoint(m_polyNodes.ChildCount() - 1, k);
	else
	{
	    IntPoint ip = m_polyNodes.Childs[(int)m_lowest.X]->Contour[(int)m_lowest.Y];
	    if (newNode->Contour[k].Y > ip.Y ||
		    (newNode->Contour[k].Y == ip.Y &&
		     newNode->Contour[k].X < ip.X))
		m_lowest = IntPoint(m_polyNodes.ChildCount() - 1, k);
	}
    }
    //------------------------------------------------------------------------------

    void ClipperOffset::AddPaths(const Paths& paths, JoinType joinType, EndType endType)
    {
	for (Paths::size_type i = 0; i < paths.size(); ++i)
	    AddPath(paths[i], joinType, endType);
    }
    //------------------------------------------------------------------------------

    void ClipperOffset::FixOrientations()
    {
	//fixup orientations of all closed paths if the orientation of the
	//closed path with the lowermost vertex is wrong ...
	if (m_lowest.X >= 0 &&
		!Orientation(m_polyNodes.Childs[(int)m_lowest.X]->Contour))
	{
	    for (int i = 0; i < m_polyNodes.ChildCount(); ++i)
	    {
		PolyNode& node = *m_polyNodes.Childs[i];
		if (node.m_endtype == etClosedPolygon ||
			(node.m_endtype == etClosedLine && Orientation(node.Contour)))
		    ReversePath(node.Contour);
	    }
	} else
	{
	    for (int i = 0; i < m_polyNodes.ChildCount(); ++i)
	    {
		PolyNode& node = *m_polyNodes.Childs[i];
		if (node.m_endtype == etClosedLine && !Orientation(node.Contour))
		    ReversePath(node.Contour);
	    }
	}
    }
    //------------------------------------------------------------------------------

    void ClipperOffset::Execute(Paths& solution, double delta)
    {
	solution.clear();
	FixOrientations();
	DoOffset(delta);

	//now clean up 'corners' ...
	Clipper clpr;
	clpr.AddPaths(m_destPolys, ptSubject, true);
	if (delta > 0)
	{
	    clpr.Execute(ctUnion, solution, pftPositive, pftPositive);
	}
	else
	{
	    IntRect r = clpr.GetBounds();
	    Path outer(4);
	    outer[0] = IntPoint(r.left - 10, r.bottom + 10);
	    outer[1] = IntPoint(r.right + 10, r.bottom + 10);
	    outer[2] = IntPoint(r.right + 10, r.top - 10);
	    outer[3] = IntPoint(r.left - 10, r.top - 10);

	    clpr.AddPath(outer, ptSubject, true);
	    clpr.ReverseSolution(true);
	    clpr.Execute(ctUnion, solution, pftNegative, pftNegative);
	    if (solution.size() > 0) solution.erase(solution.begin());
	}
    }
    //------------------------------------------------------------------------------

    void ClipperOffset::Execute(PolyTree& solution, double delta)
    {
	solution.Clear();
	FixOrientations();
	DoOffset(delta);

	//now clean up 'corners' ...
	Clipper clpr;
	clpr.AddPaths(m_destPolys, ptSubject, true);
	if (delta > 0)
	{
	    clpr.Execute(ctUnion, solution, pftPositive, pftPositive);
	}
	else
	{
	    IntRect r = clpr.GetBounds();
	    Path outer(4);
	    outer[0] = IntPoint(r.left - 10, r.bottom + 10);
	    outer[1] = IntPoint(r.right + 10, r.bottom + 10);
	    outer[2] = IntPoint(r.right + 10, r.top - 10);
	    outer[3] = IntPoint(r.left - 10, r.top - 10);

	    clpr.AddPath(outer, ptSubject, true);
	    clpr.ReverseSolution(true);
	    clpr.Execute(ctUnion, solution, pftNegative, pftNegative);
	    //remove the outer PolyNode rectangle ...
	    if (solution.ChildCount() == 1 && solution.Childs[0]->ChildCount() > 0)
	    {
		PolyNode* outerNode = solution.Childs[0];
		solution.Childs.reserve(outerNode->ChildCount());
		solution.Childs[0] = outerNode->Childs[0];
		solution.Childs[0]->Parent = outerNode->Parent;
		for (int i = 1; i < outerNode->ChildCount(); ++i)
		    solution.AddChild(*outerNode->Childs[i]);
	    }
	    else
		solution.Clear();
	}
    }
    //------------------------------------------------------------------------------

    void ClipperOffset::DoOffset(double delta)
    {
	m_destPolys.clear();
	m_delta = delta;

	//if Zero offset, just copy any CLOSED polygons to m_p and return ...
	if (NEAR_ZERO(delta))
	{
	    m_destPolys.reserve(m_polyNodes.ChildCount());
	    for (int i = 0; i < m_polyNodes.ChildCount(); i++)
	    {
		PolyNode& node = *m_polyNodes.Childs[i];
		if (node.m_endtype == etClosedPolygon)
		    m_destPolys.push_back(node.Contour);
	    }
	    return;
	}

	//see offset_triginometry3.svg in the documentation folder ...
	if (MiterLimit > 2) m_miterLim = 2/(MiterLimit * MiterLimit);
	else m_miterLim = 0.5;

	double y;
	if (ArcTolerance <= 0.0) y = def_arc_tolerance;
	else if (ArcTolerance > std::fabs(delta) * def_arc_tolerance)
	    y = std::fabs(delta) * def_arc_tolerance;
	else y = ArcTolerance;
	//see offset_triginometry2.svg in the documentation folder ...
	double steps = pi / std::acos(1 - y / std::fabs(delta));
	if (steps > std::fabs(delta) * pi)
	    steps = std::fabs(delta) * pi;  //ie excessive precision check
	m_sin = std::sin(two_pi / steps);
	m_cos = std::cos(two_pi / steps);
	m_StepsPerRad = steps / two_pi;
	if (delta < 0.0) m_sin = -m_sin;

	m_destPolys.reserve(m_polyNodes.ChildCount() * 2);
	for (int i = 0; i < m_polyNodes.ChildCount(); i++)
	{
	    PolyNode& node = *m_polyNodes.Childs[i];
	    m_srcPoly = node.Contour;

	    int len = (int)m_srcPoly.size();
	    if (len == 0 || (delta <= 0 && (len < 3 || node.m_endtype != etClosedPolygon)))
		continue;

	    m_destPoly.clear();
	    if (len == 1)
	    {
		if (node.m_jointype == jtRound)
		{
		    double X = 1.0, Y = 0.0;
		    for (cInt j = 1; j <= steps; j++)
		    {
			m_destPoly.push_back(IntPoint(
				    Round(m_srcPoly[0].X + X * delta),
				    Round(m_srcPoly[0].Y + Y * delta)));
			double X2 = X;
			X = X * m_cos - m_sin * Y;
			Y = X2 * m_sin + Y * m_cos;
		    }
		}
		else
		{
		    double X = -1.0, Y = -1.0;
		    for (int j = 0; j < 4; ++j)
		    {
			m_destPoly.push_back(IntPoint(
				    Round(m_srcPoly[0].X + X * delta),
				    Round(m_srcPoly[0].Y + Y * delta)));
			if (X < 0) X = 1;
			else if (Y < 0) Y = 1;
			else X = -1;
		    }
		}
		m_destPolys.push_back(m_destPoly);
		continue;
	    }
	    //build m_normals ...
	    m_normals.clear();
	    m_normals.reserve(len);
	    for (int j = 0; j < len - 1; ++j)
		m_normals.push_back(GetUnitNormal(m_srcPoly[j], m_srcPoly[j + 1]));
	    if (node.m_endtype == etClosedLine || node.m_endtype == etClosedPolygon)
		m_normals.push_back(GetUnitNormal(m_srcPoly[len - 1], m_srcPoly[0]));
	    else
		m_normals.push_back(DoublePoint(m_normals[len - 2]));

	    if (node.m_endtype == etClosedPolygon)
	    {
		int k = len - 1;
		for (int j = 0; j < len; ++j)
		    OffsetPoint(j, k, node.m_jointype);
		m_destPolys.push_back(m_destPoly);
	    }
	    else if (node.m_endtype == etClosedLine)
	    {
		int k = len - 1;
		for (int j = 0; j < len; ++j)
		    OffsetPoint(j, k, node.m_jointype);
		m_destPolys.push_back(m_destPoly);
		m_destPoly.clear();
		//re-build m_normals ...
		DoublePoint n = m_normals[len -1];
		for (int j = len - 1; j > 0; j--)
		    m_normals[j] = DoublePoint(-m_normals[j - 1].X, -m_normals[j - 1].Y);
		m_normals[0] = DoublePoint(-n.X, -n.Y);
		k = 0;
		for (int j = len - 1; j >= 0; j--)
		    OffsetPoint(j, k, node.m_jointype);
		m_destPolys.push_back(m_destPoly);
	    }
	    else
	    {
		int k = 0;
		for (int j = 1; j < len - 1; ++j)
		    OffsetPoint(j, k, node.m_jointype);

		IntPoint pt1;
		if (node.m_endtype == etOpenButt)
		{
		    int j = len - 1;
		    pt1 = IntPoint((cInt)Round(m_srcPoly[j].X + m_normals[j].X *
				delta), (cInt)Round(m_srcPoly[j].Y + m_normals[j].Y * delta));
		    m_destPoly.push_back(pt1);
		    pt1 = IntPoint((cInt)Round(m_srcPoly[j].X - m_normals[j].X *
				delta), (cInt)Round(m_srcPoly[j].Y - m_normals[j].Y * delta));
		    m_destPoly.push_back(pt1);
		}
		else
		{
		    int j = len - 1;
		    k = len - 2;
		    m_sinA = 0;
		    m_normals[j] = DoublePoint(-m_normals[j].X, -m_normals[j].Y);
		    if (node.m_endtype == etOpenSquare)
			DoSquare(j, k);
		    else
			DoRound(j, k);
		}

		//re-build m_normals ...
		for (int j = len - 1; j > 0; j--)
		    m_normals[j] = DoublePoint(-m_normals[j - 1].X, -m_normals[j - 1].Y);
		m_normals[0] = DoublePoint(-m_normals[1].X, -m_normals[1].Y);

		k = len - 1;
		for (int j = k - 1; j > 0; --j) OffsetPoint(j, k, node.m_jointype);

		if (node.m_endtype == etOpenButt)
		{
		    pt1 = IntPoint((cInt)Round(m_srcPoly[0].X - m_normals[0].X * delta),
			    (cInt)Round(m_srcPoly[0].Y - m_normals[0].Y * delta));
		    m_destPoly.push_back(pt1);
		    pt1 = IntPoint((cInt)Round(m_srcPoly[0].X + m_normals[0].X * delta),
			    (cInt)Round(m_srcPoly[0].Y + m_normals[0].Y * delta));
		    m_destPoly.push_back(pt1);
		}
		else
		{
		    m_sinA = 0;
		    if (node.m_endtype == etOpenSquare)
			DoSquare(0, 1);
		    else
			DoRound(0, 1);
		}
		m_destPolys.push_back(m_destPoly);
	    }
	}
    }
    //------------------------------------------------------------------------------

    void ClipperOffset::OffsetPoint(int j, int& k, JoinType jointype)
    {
	//cross product ...
	m_sinA = (m_normals[k].X * m_normals[j].Y - m_normals[j].X * m_normals[k].Y);
	if (std::fabs(m_sinA * m_delta) < 1.0)
	{
	    //dot product ...
	    double cosA = (m_normals[k].X * m_normals[j].X + m_normals[j].Y * m_normals[k].Y );
	    if (cosA > 0) // angle => 0 degrees
	    {
		m_destPoly.push_back(IntPoint(Round(m_srcPoly[j].X + m_normals[k].X * m_delta),
			    Round(m_srcPoly[j].Y + m_normals[k].Y * m_delta)));
		return;
	    }
	    //else angle => 180 degrees
	}
	else if (m_sinA > 1.0) m_sinA = 1.0;
	else if (m_sinA < -1.0) m_sinA = -1.0;

	if (m_sinA * m_delta < 0)
	{
	    m_destPoly.push_back(IntPoint(Round(m_srcPoly[j].X + m_normals[k].X * m_delta),
			Round(m_srcPoly[j].Y + m_normals[k].Y * m_delta)));
	    m_destPoly.push_back(m_srcPoly[j]);
	    m_destPoly.push_back(IntPoint(Round(m_srcPoly[j].X + m_normals[j].X * m_delta),
			Round(m_srcPoly[j].Y + m_normals[j].Y * m_delta)));
	}
	else
	    switch (jointype)
	    {
		case jtMiter:
		    {
			double r = 1 + (m_normals[j].X * m_normals[k].X +
				m_normals[j].Y * m_normals[k].Y);
			if (r >= m_miterLim) DoMiter(j, k, r); else DoSquare(j, k);
			break;
		    }
		case jtSquare: DoSquare(j, k); break;
		case jtRound: DoRound(j, k); break;
	    }
	k = j;
    }
    //------------------------------------------------------------------------------

    void ClipperOffset::DoSquare(int j, int k)
    {
	double dx = std::tan(std::atan2(m_sinA,
		    m_normals[k].X * m_normals[j].X + m_normals[k].Y * m_normals[j].Y) / 4);
	m_destPoly.push_back(IntPoint(
		    Round(m_srcPoly[j].X + m_delta * (m_normals[k].X - m_normals[k].Y * dx)),
		    Round(m_srcPoly[j].Y + m_delta * (m_normals[k].Y + m_normals[k].X * dx))));
	m_destPoly.push_back(IntPoint(
		    Round(m_srcPoly[j].X + m_delta * (m_normals[j].X + m_normals[j].Y * dx)),
		    Round(m_srcPoly[j].Y + m_delta * (m_normals[j].Y - m_normals[j].X * dx))));
    }
    //------------------------------------------------------------------------------

    void ClipperOffset::DoMiter(int j, int k, double r)
    {
	double q = m_delta / r;
	m_destPoly.push_back(IntPoint(Round(m_srcPoly[j].X + (m_normals[k].X + m_normals[j].X) * q),
		    Round(m_srcPoly[j].Y + (m_normals[k].Y + m_normals[j].Y) * q)));
    }
    //------------------------------------------------------------------------------

    void ClipperOffset::DoRound(int j, int k)
    {
	double a = std::atan2(m_sinA,
		m_normals[k].X * m_normals[j].X + m_normals[k].Y * m_normals[j].Y);
	int steps = std::max((int)Round(m_StepsPerRad * std::fabs(a)), 1);

	double X = m_normals[k].X, Y = m_normals[k].Y, X2;
	for (int i = 0; i < steps; ++i)
	{
	    m_destPoly.push_back(IntPoint(
			Round(m_srcPoly[j].X + X * m_delta),
			Round(m_srcPoly[j].Y + Y * m_delta)));
	    X2 = X;
	    X = X * m_cos - m_sin * Y;
	    Y = X2 * m_sin + Y * m_cos;
	}
	m_destPoly.push_back(IntPoint(
		    Round(m_srcPoly[j].X + m_normals[j].X * m_delta),
		    Round(m_srcPoly[j].Y + m_normals[j].Y * m_delta)));
    }

    //------------------------------------------------------------------------------
    // Miscellaneous public functions
    //------------------------------------------------------------------------------

    void Clipper::DoSimplePolygons()
    {
	PolyOutList::size_type i = 0;
	while (i < m_PolyOuts.size())
	{
	    OutRec* outrec = m_PolyOuts[i++];
	    OutPt* op = outrec->Pts;
	    if (!op || outrec->IsOpen) continue;
	    do //for each Pt in Polygon until duplicate found do ...
	    {
		OutPt* op2 = op->Next;
		while (op2 != outrec->Pts)
		{
		    if ((op->Pt == op2->Pt) && op2->Next != op && op2->Prev != op)
		    {
			//split the polygon into two ...
			OutPt* op3 = op->Prev;
			OutPt* op4 = op2->Prev;
			op->Prev = op4;
			op4->Next = op;
			op2->Prev = op3;
			op3->Next = op2;

			outrec->Pts = op;
			OutRec* outrec2 = CreateOutRec();
			outrec2->Pts = op2;
			UpdateOutPtIdxs(*outrec2);
			if (Poly2ContainsPoly1(outrec2->Pts, outrec->Pts))
			{
			    //OutRec2 is contained by OutRec1 ...
			    outrec2->IsHole = !outrec->IsHole;
			    outrec2->FirstLeft = outrec;
			    if (m_UsingPolyTree) FixupFirstLefts2(outrec2, outrec);
			}
			else
			    if (Poly2ContainsPoly1(outrec->Pts, outrec2->Pts))
			    {
				//OutRec1 is contained by OutRec2 ...
				outrec2->IsHole = outrec->IsHole;
				outrec->IsHole = !outrec2->IsHole;
				outrec2->FirstLeft = outrec->FirstLeft;
				outrec->FirstLeft = outrec2;
				if (m_UsingPolyTree) FixupFirstLefts2(outrec, outrec2);
			    }
			    else
			    {
				//the 2 polygons are separate ...
				outrec2->IsHole = outrec->IsHole;
				outrec2->FirstLeft = outrec->FirstLeft;
				if (m_UsingPolyTree) FixupFirstLefts1(outrec, outrec2);
			    }
			op2 = op; //ie get ready for the Next iteration
		    }
		    op2 = op2->Next;
		}
		op = op->Next;
	    }
	    while (op != outrec->Pts);
	}
    }
    //------------------------------------------------------------------------------

    void ReversePath(Path& p)
    {
	std::reverse(p.begin(), p.end());
    }
    //------------------------------------------------------------------------------

    void ReversePaths(Paths& p)
    {
	for (Paths::size_type i = 0; i < p.size(); ++i)
	    ReversePath(p[i]);
    }
    //------------------------------------------------------------------------------

    void SimplifyPolygon(const Path &in_poly, Paths &out_polys, PolyFillType fillType)
    {
	Clipper c;
	c.StrictlySimple(true);
	c.AddPath(in_poly, ptSubject, true);
	c.Execute(ctUnion, out_polys, fillType, fillType);
    }
    //------------------------------------------------------------------------------

    void SimplifyPolygons(const Paths &in_polys, Paths &out_polys, PolyFillType fillType)
    {
	Clipper c;
	c.StrictlySimple(true);
	c.AddPaths(in_polys, ptSubject, true);
	c.Execute(ctUnion, out_polys, fillType, fillType);
    }
    //------------------------------------------------------------------------------

    void SimplifyPolygons(Paths &polys, PolyFillType fillType)
    {
	SimplifyPolygons(polys, polys, fillType);
    }
    //------------------------------------------------------------------------------

    inline double DistanceSqrd(const IntPoint& pt1, const IntPoint& pt2)
    {
	double Dx = ((double)pt1.X - pt2.X);
	double dy = ((double)pt1.Y - pt2.Y);
	return (Dx*Dx + dy*dy);
    }
    //------------------------------------------------------------------------------

    double DistanceFromLineSqrd(
	    const IntPoint& pt, const IntPoint& ln1, const IntPoint& ln2)
    {
	//The equation of a line in general form (Ax + By + C = 0)
	//given 2 points (x^1,y^1) & (x^2,y^2) is ...
	//(y^1 - y^2)x + (x^2 - x^1)y + (y^2 - y^1)x^1 - (x^2 - x^1)y^1 = 0
	//A = (y^1 - y^2); B = (x^2 - x^1); C = (y^2 - y^1)x^1 - (x^2 - x^1)y^1
	//perpendicular distance of point (x^3,y^3) = (Ax^3 + By^3 + C)/Sqrt(A^2 + B^2)
	//see http://en.wikipedia.org/wiki/Perpendicular_distance
	double A = double(ln1.Y - ln2.Y);
	double B = double(ln2.X - ln1.X);
	double C = A * ln1.X  + B * ln1.Y;
	C = A * pt.X + B * pt.Y - C;
	return (C * C) / (A * A + B * B);
    }
    //---------------------------------------------------------------------------

    bool SlopesNearCollinear(const IntPoint& pt1,
	    const IntPoint& pt2, const IntPoint& pt3, double distSqrd)
    {
	//this function is more accurate when the point that's geometrically
	//between the other 2 points is the one that's tested for distance.
	//ie makes it more likely to pick up 'spikes' ...
	if (Abs(pt1.X - pt2.X) > Abs(pt1.Y - pt2.Y))
	{
	    if ((pt1.X > pt2.X) == (pt1.X < pt3.X))
		return DistanceFromLineSqrd(pt1, pt2, pt3) < distSqrd;
	    else if ((pt2.X > pt1.X) == (pt2.X < pt3.X))
		return DistanceFromLineSqrd(pt2, pt1, pt3) < distSqrd;
	    else
		return DistanceFromLineSqrd(pt3, pt1, pt2) < distSqrd;
	}
	else
	{
	    if ((pt1.Y > pt2.Y) == (pt1.Y < pt3.Y))
		return DistanceFromLineSqrd(pt1, pt2, pt3) < distSqrd;
	    else if ((pt2.Y > pt1.Y) == (pt2.Y < pt3.Y))
		return DistanceFromLineSqrd(pt2, pt1, pt3) < distSqrd;
	    else
		return DistanceFromLineSqrd(pt3, pt1, pt2) < distSqrd;
	}
    }
    //------------------------------------------------------------------------------

    bool PointsAreClose(IntPoint pt1, IntPoint pt2, double distSqrd)
    {
	double Dx = (double)pt1.X - pt2.X;
	double dy = (double)pt1.Y - pt2.Y;
	return ((Dx * Dx) + (dy * dy) <= distSqrd);
    }
    //------------------------------------------------------------------------------

    OutPt* ExcludeOp(OutPt* op)
    {
	OutPt* result = op->Prev;
	result->Next = op->Next;
	op->Next->Prev = result;
	result->Idx = 0;
	return result;
    }
    //------------------------------------------------------------------------------

    void CleanPolygon(const Path& in_poly, Path& out_poly, double distance)
    {
	//distance = proximity in units/pixels below which vertices
	//will be stripped. Default ~= sqrt(2).

	size_t size = in_poly.size();

	if (size == 0)
	{
	    out_poly.clear();
	    return;
	}

	OutPt* outPts = new OutPt[size];
	for (size_t i = 0; i < size; ++i)
	{
	    outPts[i].Pt = in_poly[i];
	    outPts[i].Next = &outPts[(i + 1) % size];
	    outPts[i].Next->Prev = &outPts[i];
	    outPts[i].Idx = 0;
	}

	double distSqrd = distance * distance;
	OutPt* op = &outPts[0];
	while (op->Idx == 0 && op->Next != op->Prev)
	{
	    if (PointsAreClose(op->Pt, op->Prev->Pt, distSqrd))
	    {
		op = ExcludeOp(op);
		size--;
	    }
	    else if (PointsAreClose(op->Prev->Pt, op->Next->Pt, distSqrd))
	    {
		ExcludeOp(op->Next);
		op = ExcludeOp(op);
		size -= 2;
	    }
	    else if (SlopesNearCollinear(op->Prev->Pt, op->Pt, op->Next->Pt, distSqrd))
	    {
		op = ExcludeOp(op);
		size--;
	    }
	    else
	    {
		op->Idx = 1;
		op = op->Next;
	    }
	}

	if (size < 3) size = 0;
	out_poly.resize(size);
	for (size_t i = 0; i < size; ++i)
	{
	    out_poly[i] = op->Pt;
	    op = op->Next;
	}
	delete [] outPts;
    }
    //------------------------------------------------------------------------------

    void CleanPolygon(Path& poly, double distance)
    {
	CleanPolygon(poly, poly, distance);
    }
    //------------------------------------------------------------------------------

    void CleanPolygons(const Paths& in_polys, Paths& out_polys, double distance)
    {
	out_polys.resize(in_polys.size());
	for (Paths::size_type i = 0; i < in_polys.size(); ++i)
	    CleanPolygon(in_polys[i], out_polys[i], distance);
    }
    //------------------------------------------------------------------------------

    void CleanPolygons(Paths& polys, double distance)
    {
	CleanPolygons(polys, polys, distance);
    }
    //------------------------------------------------------------------------------

    void Minkowski(const Path& poly, const Path& path,
	    Paths& solution, bool isSum, bool isClosed)
    {
	int delta = (isClosed ? 1 : 0);
	size_t polyCnt = poly.size();
	size_t pathCnt = path.size();
	Paths pp;
	pp.reserve(pathCnt);
	if (isSum)
	    for (size_t i = 0; i < pathCnt; ++i)
	    {
		Path p;
		p.reserve(polyCnt);
		for (size_t j = 0; j < poly.size(); ++j)
		    p.push_back(IntPoint(path[i].X + poly[j].X, path[i].Y + poly[j].Y));
		pp.push_back(p);
	    }
	else
	    for (size_t i = 0; i < pathCnt; ++i)
	    {
		Path p;
		p.reserve(polyCnt);
		for (size_t j = 0; j < poly.size(); ++j)
		    p.push_back(IntPoint(path[i].X - poly[j].X, path[i].Y - poly[j].Y));
		pp.push_back(p);
	    }

	solution.clear();
	solution.reserve((pathCnt + delta) * (polyCnt + 1));
	for (size_t i = 0; i < pathCnt - 1 + delta; ++i)
	    for (size_t j = 0; j < polyCnt; ++j)
	    {
		Path quad;
		quad.reserve(4);
		quad.push_back(pp[i % pathCnt][j % polyCnt]);
		quad.push_back(pp[(i + 1) % pathCnt][j % polyCnt]);
		quad.push_back(pp[(i + 1) % pathCnt][(j + 1) % polyCnt]);
		quad.push_back(pp[i % pathCnt][(j + 1) % polyCnt]);
		if (!Orientation(quad)) ReversePath(quad);
		solution.push_back(quad);
	    }
    }
    //------------------------------------------------------------------------------

    void MinkowskiSum(const Path& pattern, const Path& path, Paths& solution, bool pathIsClosed)
    {
	Minkowski(pattern, path, solution, true, pathIsClosed);
	Clipper c;
	c.AddPaths(solution, ptSubject, true);
	c.Execute(ctUnion, solution, pftNonZero, pftNonZero);
    }
    //------------------------------------------------------------------------------

    void TranslatePath(const Path& input, Path& output, const IntPoint delta)
    {
	//precondition: input != output
	output.resize(input.size());
	for (size_t i = 0; i < input.size(); ++i)
	    output[i] = IntPoint(input[i].X + delta.X, input[i].Y + delta.Y);
    }
    //------------------------------------------------------------------------------

    void MinkowskiSum(const Path& pattern, const Paths& paths, Paths& solution, bool pathIsClosed)
    {
	Clipper c;
	for (size_t i = 0; i < paths.size(); ++i)
	{
	    Paths tmp;
	    Minkowski(pattern, paths[i], tmp, true, pathIsClosed);
	    c.AddPaths(tmp, ptSubject, true);
	    if (pathIsClosed)
	    {
		Path tmp2;
		TranslatePath(paths[i], tmp2, pattern[0]);
		c.AddPath(tmp2, ptClip, true);
	    }
	}
	c.Execute(ctUnion, solution, pftNonZero, pftNonZero);
    }
    //------------------------------------------------------------------------------

    void MinkowskiDiff(const Path& poly1, const Path& poly2, Paths& solution)
    {
	Minkowski(poly1, poly2, solution, false, true);
	Clipper c;
	c.AddPaths(solution, ptSubject, true);
	c.Execute(ctUnion, solution, pftNonZero, pftNonZero);
    }
    //------------------------------------------------------------------------------

    enum NodeType {ntAny, ntOpen, ntClosed};

    void AddPolyNodeToPaths(const PolyNode& polynode, NodeType nodetype, Paths& paths)
    {
	bool match = true;
	if (nodetype == ntClosed) match = !polynode.IsOpen();
	else if (nodetype == ntOpen) return;

	if (!polynode.Contour.empty() && match)
	    paths.push_back(polynode.Contour);
	for (int i = 0; i < polynode.ChildCount(); ++i)
	    AddPolyNodeToPaths(*polynode.Childs[i], nodetype, paths);
    }
    //------------------------------------------------------------------------------

    void PolyTreeToPaths(const PolyTree& polytree, Paths& paths)
    {
	paths.resize(0);
	paths.reserve(polytree.Total());
	AddPolyNodeToPaths(polytree, ntAny, paths);
    }
    //------------------------------------------------------------------------------

    void ClosedPathsFromPolyTree(const PolyTree& polytree, Paths& paths)
    {
	paths.resize(0);
	paths.reserve(polytree.Total());
	AddPolyNodeToPaths(polytree, ntClosed, paths);
    }
    //------------------------------------------------------------------------------

    void OpenPathsFromPolyTree(PolyTree& polytree, Paths& paths)
    {
	paths.resize(0);
	paths.reserve(polytree.Total());
	//Open paths are top level only, so ...
	for (int i = 0; i < polytree.ChildCount(); ++i)
	    if (polytree.Childs[i]->IsOpen())
		paths.push_back(polytree.Childs[i]->Contour);
    }
    //------------------------------------------------------------------------------

    std::ostream& operator <<(std::ostream &s, const IntPoint &p)
    {
	s << "(" << p.X << "," << p.Y << ")";
	return s;
    }
    //------------------------------------------------------------------------------

    std::ostream& operator <<(std::ostream &s, const Path &p)
    {
	if (p.empty()) return s;
	Path::size_type last = p.size() -1;
	for (Path::size_type i = 0; i < last; i++)
	    s << "(" << p[i].X << "," << p[i].Y << "), ";
	s << "(" << p[last].X << "," << p[last].Y << ")\n";
	return s;
    }
    //------------------------------------------------------------------------------

    std::ostream& operator <<(std::ostream &s, const Paths &p)
    {
	for (Paths::size_type i = 0; i < p.size(); i++)
	    s << p[i];
	s << "\n";
	return s;
    }
    //------------------------------------------------------------------------------

} //ClipperLib namespace

#if defined(__GNUC__) && !defined(__clang__)
#  pragma GCC diagnostic pop /* end ignoring warnings */
#elif defined(__clang__)
#  pragma clang diagnostic pop /* end ignoring warnings */
#endif

// Local Variables:
// tab-width: 8
// mode: C++
// c-basic-offset: 4
// indent-tabs-mode: t
// c-file-style: "stroustrup"
// End:
// ex: shiftwidth=4 tabstop=8
